So we've got to pick the fruits we want
to harvest off the tree which will be

the products.

We've got to find out
the pathways to get there.

We've got to look at the feasibility of
the process the control structure and

all the other listed rise that doesn't
mean that they're afterthoughts but

the resource conservation and
environment safety and

health strategies need to be
taken to account as well.

Each of those problems are pretty
complex and hard to handle even more so

if we start looking at
them at the same time.

So there's a lot of work in the systems
community trying to address even

just small combination of these.

So.

When you said getting into the math of
it and that's the part I'm going to

skip over pretty quickly but
generally you can describe any process or

product design problem by series
of these five six equations

in a very simplified form you'll have
some kind of an objective function.

You'll have a process or a product model
maybe even both you have some equality in

inequality constraints and
some structural constraints.

There's two main ways
that you can solve this.

You can do it based on heuristics or

knowledge which means you try
to come up with a feasible but

not necessarily optimal solution where
you can do the brute force mathematics

of my station where you solve the
objective function and the constraints.

The problem with the optimization approach
is that depending on the complexity of

the problem you may not end
up with a solution at all.

So another way to do it is to look at
a hybrid solution approach where you use

knowledge or he risks a kind of bound the
variables a little bit before you invoke

the numerical solver.

Excuse me.

However regardless of
Reddit approach you take.

The key ingredient is going to
be the process or the product

model that always is going to be there and
it's going to be that model that dictates

the kind of solutions you can get and
the complexity of the solution step.

So what I want to do is spend
just a couple of minutes on

the writers that might.

Play particularly the property
models because that's usually where

all the complexity is when we're trying to
solve these kinds of integrated problems.

So if you go back to the product tree.

Different constitutive equations or
models cover.

Different areas of the product range.

So some will be best at handling
a certain class of of chemicals and

others were high and or another class so

have just try to illustrate those
with three different colors.

There's a couple of questions.

When you choose the property model
you basically implicitly have chosen

the search space that
you can handle as well.

The question is do we know enough to
drive one single model credibly not and

even if we did the time it would take to
develop one that would cover everything

and probably not be worth the investment
compared to use and a couple of different

hybrid approaches to the question that we
would like to address from a systems level

perspective is whether we can
solve simulation and or my station

problems where you can use multiple
models to represent the same variable.

So in order to do that we need to
look at what use of models for.

Generally the product probably model.

Represent the physical properties as
a function of the intensive variables

like temperature pressure composition and
the component I.D.'s So

it provides basically a service to your
process model the process model ask for

physical properties and
it will provide the information

in terms of temperature pressure
conversation in the confines.

And the past as matter is just some
box relating the raw materials

to the products.

If you serve in more than once.

Then it's a simulation.

Whether or not you do that an aspirin or
a by hand or whatever.

Anytime you solve the same set
of equations more than once.

It's basically a simulation.

A simulation you use some set of
design parameters guess the angle and

ices that up a bit.

And as you've a the design
parameters you evaluate the results.

OK.

That you can feed into an algorithm
that handles synthesis and design.

In this place the property model provides
a service through the process model.

Now back in the eighty's or
so a lot of work was done

on trying to use the synthesis methods as
a means of bounding our design targets and

the feasibility of the different
approaches as well.

When we do that the property
model will provide advice.

On the ranges that we can expect
the properties to have and so on.

So there's have been the two main ways

that we have used property models in
the past where we would like to do.

Is use them in a as part of
the solution directly and

not just as an embedded
part of the equations but

in order to do that we would need
to reverse the flow of information.

So that we can solve the process
model in terms of properties and

the property model now
returns intensive variables

meaning the temperature of the pressure
conversations and or the compound I.D.'s.

But that is a different way of approaching
it from how we've done it in the past.

The beauty of it is that in
general by decoupling these two.

The size of the problem
becomes significantly

reduced because all of
the non-linearity and

generally there is buried inside the
property model not so much in the process

model because that mostly consists
of balancing constraint equations.

So we came up with I can't
claim all the credit for this.

I'd like to but I can't.

My Ph D. advisor was the one that came
up with the first part of it which was

the reverse problem from relation.

It basically provides this computationally
more efficient solution strategy.

What we're doing is a targeting approach
where we try to target the actual solution

before we do any complex calculations and
it allows us to

decouple the two types of of the equations
and I'll show you that in just a second.

The beauty of do.

And a targeting approach is that it.

It relieves a little bit of that.

Inherent literature of
nature that design has.

So this is conceptually
how it works you decouple

the constitutive equations which
includes all the phenomena and

cons property models and here from
the balancing constraint equation is

when you do that you take one
conventional forward problem.

And reformulated as to backwards problems.

So what you do is you solve the balancing
constraint equations to identify

the targets basically doing
a reverse simulation.

That gives you the design targets or
the values of the constitutive variables.

And then the second reverse problem is
you solve the constituted equations to

match the targets.

Now to the benefit of this is that
every time you match the targets.

You don't have to resolve
the bouncing constraint equations.

It also means that you can have any number
of different property models to represent

the same constitute variables here.

So you don't need to solve
those again if you know

the targets all you do is
decouple the two problems.

So for the target and
then try to match and

it makes it a lot more efficient
from a computation standpoint.

OK Now the constitutive a was one way of
representing that a physical properties

and that's the part I'm
going to focus on today.

So why would you want to do design
based on properties in the first place.

Rather a lot of processes that are driven
by physical properties rather than

chemical components.

And a lot of that motivation for this work
came out of my time in Auburn initially

when we started working
with the paper industry.

Now as General Chemical engineers all
you students are used to basically

equating quality with purity.

And the paper makers can't do that you can
have one hundred percent pure cellulose

going into and out of the paper machine
and the product can be worthless.

So stand.

Design techniques that equate you know
composition as a means of quality.

Pretty much fail at designing these kinds
of processes because the quality depends

on physical properties like opacity
activity and other metrics that are not

related to the purity of the cellulose but
depending on physical properties and

stuff like fiber length in a kind of
to video the fibers and so forth.

So there wasn't a systematic
way of handling that.

So that was what we wanted to
start out trying to address and

a lot of the performance objectives
are described in terms of properties as

well because really in the in the design.

Field.

You don't care much where the name of
a compound is until you have to buy

it up until that point it serves a purpose
meaning it has certain properties where

functionality is that you mean if you
need to do a solvent extraction you

really don't care.

Conceptually whether it's called Benzino
tell you when until you have to buy it up

until that point you worry
about how well it does the job.

So those are based on the properties and
so

much on the name of
the identity of the components.

When you get into problem electro
design in particular it's all based on

properties.

So there was an opportunity that we
thought to look at the properties

as an interface between the types
of different properties.

Now that we came up with was
what we call property clusters.

It is not meant to replace
any of the composition

based techniques that we all know and
love.

Because the types of problems
that the composition based

techniques can handle they do very well.

So this is meant to extend those kinds of

methodologies into the types of products
or problems that we can't solve.

So we wanted to come up
with a way that we could

reduce the dimensionality of the problem.

In order to visualize it
because that is very helpful

in trying to gain some insights.

We generally do on the property estimation
for the molecular design using.

Contribution but I'll show you at least
in passing some examples of other methods

that we've used those of you who watched
Professor disco's seminar here in November

would have seen a lot of the work that
we've done on that as well we've used

a lot of his methods for representing
our nontraditional properties.

So basically what this provides us
is a framework that allows us to

approach both the molecular
design problem and

the process design problem from
the properties perspective.

So I'm not going to detail all the.

The math that goes into this because.

It's really not that interesting and
the truth is not that it complex.

So it's not worth the time but
basically what you do

is you basically you take
the physical properties and

you rearrange the description into
a combination of Euclidean vector and

a scalar function and but you end up with

these conserved surrogate properties
that all have linear mixing roles.

Now is the theme of analysis among
you're going to flinch when you hear

the word linear makes in roles
because that rarely happens.

And that is true what we do instead

is write it as a linear
mixing of non-linear terms.

The easiest way to explain that
is to use something like density.

Density does not have a linear mixing up.

But inverse density does so

you can hide the non-linearity in
the functionality description.

When you do that but

you basically do is reverse the
representation of the composition space.

Normally we would represent on a turn or

a diagram of the species on the very C's
and the properties inside the space.

We basically reversed
that a make one turn.

Put the functions of the properties
on the various Cs and

the components on the inside.

That has a lot of benefits.

When you have money and makes the rules
even if the terms themselves are nonlinear

that means that all the mixing operations
are straight lines which helps you

do simple mixing up to my
station directly visually.

I'm going to show you a little bit
of the algorithm here basically

there's a linear I say should step
then and normalization step and

then the original formulation required
the identification of this augmented

property index which was named a U.
peek as it was developed at all but

instead of an A.P.I.
I can't claim credit for that either.

That was Dr how long he's idea but

I thought it was comical so
we left it that way.

OK but there are a few conditions that

need to be met when you're solving
these problems particularly visually.

The first one.

You have to be inside
the feasibility region for

a given unit that you want to feed it
to that provides you the first level

then there's a sufficient condition that
at the same point you have to match that

value of this index and
the analogy you can

use is that the location corresponds
to a set of three mass fractions.

The only way that you get a unique
solution is if the total mass remains

the same for both solutions.

OK So there's a it's a similar analogy for
that.

OK show an example.

The first one we did was from
the paper making industry.

And it's a simple recycle problem

you have some fibers that
go into the paper machine.

Some of it turns into papers all
of it is rejected then it's pulped

served some of it goes to waste and
some are potential for recycle.

So the streams are categorized not by
the purity of the Cellulose Fibers but

by the properties of it.

And the objectionable material
was basically just to

a mass fraction However the it's.

Fission and reflectivity kind of
could come monk papers theory.

And then you're given some information on
the properties of the flows of the fibers

in the pro five years and the conditions
of the paper machine that they can accept.

So there's a lot of data in a table.

No worries.

The interesting thing of
these three numbers and

the fact that we have two linear and
one non-linear property

description but the beauty of it is and
this is something that Professor Ralph.

Can probably comment on I'm sure
he teaches in his courses as well

you can look at a lot of this data.

The beauty of this approach when you think
of it from a systems perspective is that

if you have a paper machine that requires
a minimum of one hundred tons to go into

the feed and
we have a maximum of thirty tons of

recyclable material left no matter
how well we design anything.

We're still going to need seventy tons
of fresh material to be fed in but

that's an important target
to know because that

is something we can compare all
of our other solutions against.

So we have two different ways we can
do this we can do a direct recycle

of the fibers.

Or maybe do some kind of change
to them and then recycle them.

So when you take all the data and

you translate it into the property space
this is what it ends up looking like.

The constraints on the paper
machine becomes a region and

here the fresh fibers are located here.

The recycle fibers are located here.

And since our mixing
operations are straight lines.

It's pretty easy to find
out which one will maximize

the recycler of the of
the profilers it ends up being

the point where you have the longest
on for the profilers you

can then back accolade the flow rate it
ends up being eighty three times an hour.

You know that the maximum I recycle
we can do would give a fresh five or

recycle of seventy.

So we would have to do something to change
the properties of the broad fibers.

In order to get there.

So you can then solve the problem
backwards again with a new target saying

that we want to be able to recycle all of
the broke fibers when you do that you have

to move the cut the properties to
this point again this is all solved.

Visually you don't have to worry
about what the properties are but

then they're usually back
calculated after that.

Now I gotta admit I'm not a paper person.

So I don't know what the physical or

chemical treatment it is that is necessary
to move the absorption causation and

reflectivity to these values but
to the benefit is that we were

able to target this without having to
do a lot of detailed calculations.

So that was going to pass this on to
the paper makers and they can come

up with some technologies for doing that
they know that a lot better than we do.

So once we had the process side.

Want to link this to the molecular design
that we've been doing on other topics.

You will notice that the the operator
the property operators.

The functional description of
them look very much like what

we're used to seeing for
group contribution.

Group kind of using methods generally take
the number of occurrences of a given group

times the contribution of that group and
you add it all up you get the total

property for so
we want to figure out a way that

we can combine the two the beauty of it
is once you have it in an operator form.

The rest of the math remains the same.

So it should be possible to represent
both problems on the same platform and

that's basically what we did you end up
with a different representation of the.

The lever arm that you use graphically was

now becomes the location of
the combined molecule when you add

two fragments together rather than
the mixing ratio of two strains.

So there's one way you
can illustrate this.

This is a simplified
representation of one.

The properties are that we want
to give an molecule to have.

And these are the Canada
fragments we have available.

So we could need to move inside this
region so let's say we combine not mix but

combine G one and
G two that would get us somewhere here.

Then we need to move in this direction.

So we could add fragmented
G three which moves us.

Into the space that we need However in
this case we still have at conceptually

one for you.

Beyond which we can have so we need to
add another terminating group and this

would be G four we end up with a molecule
here that ends up inside the region.

So you can do all this usually by
just keeping track of the free bonds

pretty straightforward.

There's going to be some
conditions you need

to have no Freedmen's left
over when you're done.

Otherwise it's not a complete molecule it.

The location of the final molecule
should be inside the region.

It should match at least the five
minute index of the region.

The range of it.

And the reason for
that is that you have some properties in

there that are not calculated
directly from group contribution.

There's only a limited number
of properties that you can

predict using group contribution.

And some of them need to be double checked
against the real property is one of them

is like vapor pressure.

I'll show you that in a second but they
pressure can't be predicted from group

contribution but you can use an empirical
correlation between vapor pressure and

willing point and boiling point can be
predicted from group contributions but

you need to double check that
the translation between the two doesn't

lose any information.

So I think sample if I show you
just a molecular synthesis.

This was started as a kind of
a traditional and mixed in.

It's were not linear programming problem
by looking Chinese group that it was

that when he was stood
University Connecticut.

But design of a blanket wash solvent for
resin printing ink and we saw.

Solve the exact same problem except
we did it all graphically and so

the first issue is you have seven
possible groups available and

there's a maximum chain length
of seven groups in this case.

And then there are five
properties that we need to match.

OK here of a price.

Ation boiling point Melting Point base for
pressure and

some other one that I for
mine and I can remember.

Anyway.

My bad.

To solve it graphically because that was
the intent of the method in the first

place so that means we're limited to three
properties so we did three of them and

we want to use the remaining two
Ask meaning criteria afterwards.

OK so we use heat of vaporization and
the two temperatures boiling and

melting temperatures for
the the graphical approach and

then we left they pressure inside the
ability and screen criteria afterwards.

So from kind of usual you get the
expressions for the different properties.

They can then be translated into
the molecular property operators with some

appropriately chosen reference
values which basically just

brings everything to
the same order of magnitude.

When you know on the rise it.

So this is where the property
constraints of the solvent need to fall.

Here's a location of the different
groups that sin and she had chosen.

And then you can basically just start
building combinations until you no longer

have any free bonds.

There's a variety of them.

Now.

If you're thinking about is to
compare the visual approach

with makes them a job and
only optimization you can see.

But most of the fragments are already
inside the constraints so

it shouldn't have been a particularly
hard all to my station problem for

them to solve and it wasn't bad.

You don't.

We get that when you just
look at the constraints.

So we designed eleven candidate
molecules doing this.

Then there's a couple of additional
checks that need to be done.

They all are inside the region so
that takes care of the first condition.

They also have no feed
on is that second one.

Then there's a couple of checks
the bottom three fall out because

of the values of the index.

Then the rest of them all eight of
them satisfy everything including

the non group contribution
based properties.

So that means they're at least
candidates for further study.

So members of the eight candidates
seven of them are the same as right

at Cheney and and Senate came up with and
then there's one more thing.

And that was screened out
because it's final and

because of what they wanted for they
didn't actually include it in the family

lation when this all did
with out to my station.

But it does satisfy all the property
constraints that were specified except it

would not be feasible for that application
how it fell out of the opposition

approach I'm not sure but
the other seven are exactly the same.

So now it shouldn't be a surprise that

what we want to do is really
link the two approaches.

We've looked at it from a process side and
we look at it from a molecular side.

So what we'd like to do is solve
the process design in terms of

the property targets.

Then design the corresponding
molecules that we need.

OK So
this is an example where we did that.

It's a matter of degree
sing process where.

An organic solvent is used in a degree.

Certain.

And then a lot of it is evaporated
as a mixture of off gases.

And an issue from relation to.

Provided to be fired.

We wanted to see if we
could then condense it.

And use it for

something to reduce the amount of
fresh selling that we would need.

OK And then we want to do it graphically
so we just chose three properties

to represent a strain the amount of sulfur
in there for corrosion purposes the middle

of volume for you know pumping in and
recovery aspects of the vapor pressure.

So we had some constraints
on the unit how much.

Software could be allowed in there.

What the volume should be in
the vapor pressure and then we had to

learn to make some rules for the whole
of volume and the amount of sulfur and

then they nonlinear making room for
the vapor pressure.

So you translate the data you
end up with something like this.

The constraints on the degrees and
unit makes for this region right here.

And then we had some data of the
properties of the concept as a function

of temperature.

If you think about the V.O.C.
has been a mixture of organics

you change the temperature of different
species are going to condense that's going

to have a an effect on
the properties of the concept.

So it's for station purposes we chose to
run the condenser at five hundred Kelvin.

And so that gives us this point since all
the mixing operations a straight line is

that gives us a target for
where the boundaries are for

different lines that could go
through that a greasing unit and

still makes with the five hundred K.
Conn and said.

And then we made it simpler ourselves and
said we're not going to have any suffering

there by just eliminating any sulfur
containing not molecular fragments so

that means that our property targets
are is everything between point A and

point B. on this axis because
sulphur moves in this direction and

in the trying to phase diagram.

So we now have the property targets.

We want to pull in.

Me a group contribution based
properties that we have

any of the non group contribution based
properties need to be translated and

then we need to solve
the molecular theirs on.

So our targets and I think it will be
in the way over here is the software so

by not having any software in the groups
that gives us a degree of freedom and

still be able to solve it graphically so
we added the head of a price.

Ation.

As another property that we
wanted the solvent to have.

So there's like I said before
vapor pressure cannot be predicted

directly from group contribution but
you can link it to the boiling point.

Via this kind of empirical
expression here.

So now we have the all the molecular
property operators here.

We have a selection of seven
groups that we can use and

this time we have at least
two outside the range.

We can design a series of candidates.

And then check for the different
kinds of feasibility they are all

inside the feasibility region and
they all have complete.

They and c So there is no more free bonds.

To fall outside the index range and

two of them when you actually
predicted the vapor pressure for

those components they
fell outside that range.

So we're left with three.

So we have two different tones and
and want to cover so I guess it.

Now we can place those back on
the original diagram because we know what

its properties are and we know that all
the mixing operations are straight lines.

We want to maximize the amount
of recycle that we could do so

that means it's the one
with the shortest arm for

the fresh solvents which means it's
the one in the middle in this case.

But it's a very simple way of the.

Pushing the problem from both sides.

Now granted.

It doesn't allow you to solve every kind
of problem you need to be able to scribe

both the process and the molecules from
the properties perspective in order to do

this but
it does provide at least the first

generally unified framework for
addressing this from both sides so.

The way from member Malik you will see and

start looking at more
general product design.

Which just as design of
structured products.

The National Research Council came out
with this set of findings about a year and

a half ago.

They started coming up with what are
the challenges that our community faces

that we need to be able
to predict structures and

properties from fundamental principles but
that's always been.

The Holy Grail for engineers but

what we really want to do is
to complement experimental and

theoretical approaches experiments
are very expensive time consuming and

the vast size of the search space
makes it almost impossible to go.

Test one thing see if it works tests and
other and so on.

So we'd like to be able to compliment
that was something so real theory.

But then as a lot of the research
that's going on in this place shows.

There's a variety of different
scales that we now have to address

which we haven't had to before.

So Michael Hill.

Read a paper a few years before the
National Research Council about what it

is that the systems community could do.

We should be able to combine the risk.

There's an optimization.

The one thing that will be different from
what we're used to is that no longer will

we describe everything in terms
of physical properties but

rather performance
attributes which are much.

Harder to handle than the physical
properties because the a lot of

the professions attributes are going
to be consumer desires and

stuff like that that we don't really
have a handle on how to predict.

But what we would need at some point
is a new methodology that we're not

eliminate the need for experimentation.

That will help to guide and
focus what experiments to run.

So that's when you get
into multi scale systems.

I'm not going to spend a lot
of time on that but really

when you want to do design for
products you're dealing

with all the different scales both from
the process side and the molecular design.

So the question is can we match
all the scales at the same time.

This is what I showed you before we
basically tried to solve the process

design problem in terms of
some initial property targets

then solve them like a design problem and
feed the molecules back.

From it to scale that
doesn't quite work that way.

It's not that easy.

However.

We could use probably the properties as
an interface between the different types

of problems.

So you can use fundamental principles for
the process designed to generate some

property information consumer add
to can probably be translated

to properties using some kind of metrics
and I'll show you an example of that here

in a little bit microstructure is where
you get into the more structured products.

There's a lot of work being done on course
training and other times not as for

doing this we're still left with kind of
you know into season stuff like that for

the molecular scale and then the atomistic
methods for doing like remodeling like I

mentioned so on and fundamental ab
initio methods which is not something

I'm going to talk about at all but
there are a lot of good work being done.

In those areas but it should be
possible to make all those through.

Intake of the properties.

Which is a thing that is not usually
looked at in that perspective.

So what we're focusing on is that linkage
between the complementary experimental and

theoretical approaches as they were
outlined by the Research Council.

So we're looking at pathways.

There is the key metric in fairness which
is the part I'm going to talk about today

mostly I'll talk about mixture
design of experiments.

And some semi empirical models
which I won't cover but

higher order group
contribution is one of them.

Connectivity indices methods and
other Q Sark US P.R.

methods and molecular Bethia
which is basically a variation

on the theme that Dr Biscoe presented in
November we use a lot of the the signature

descriptors to describe the more
nontraditional properties as well.

So.

I'll just quickly how
the general framework looks.

Basically there's an empirical
method that we try to

translate that should be targets.

Into some design targets that
is not a trivial thing to do and

all we did basically was set
up a generalized framework for

doing this is going to be very vacay
specific because the linkage between.

The consumer to buttes and the physical
properties are more are more or

less case specific so you can say that for

paper the tactile feel that the consumer
wants is related to a certain property

that is going to be the same property
if you start talking about a lotion.

So there's going to be
a lot of case specific and

data driven information there.

But you could also map some
of this down using a lot of

other information that are being used
spectrum information and so on for

the molecular makeup a specific
specifically for Structured Products like.

Different kinds of composites and so on.

There's a lot of data available but
it needs to be processed in.

A different way.

So I'm not going to spend any more time.

On this what I'd like to show you instead
is a bit about the design of experiments.

Now a lot of you probably do experiments.

And you've done.

Design of experiments you try to
find out response surface Pods and

find out where your sweet spots are and
so on.

And I know that Dr Lee and Dr Ralph are
doing some really interesting stuff on how

to handle the uncertainties in this
what I'm going to show you is a way of

handling some of the common
toil explosion instead.

So next to design is the one I want
to focus on what you try to do and

which is basically deal we are all the
fragments or the compositions to add up to

one as you know the difference between
a normal day a week and make sure you eat.

And what you're trying to do is come
up with a way that you can represent

the physical phenomena using
the minimum number of experiments.

So you can use stuff like box thinking
type designs and so on to try to explore

the search space but you end up with an
expectation that will allow you to relate

some kind of property to a function
of the amount of the constituents.

OK.

So you run some experiments
you collect some data.

And now we have some data for

the responses as a function
of a series of chosen points.

Then we try to do a bad model from
that and there's main two main ways of

doing that there's the polynomial
models and the canonical models.

But they try to do
the same thing represent

the responses that we got as a function
of the compositions of the constituents.

And then we try to use it for prediction.

That's all good now.

The best separate from
coming to explosion.

If you have seven components
then that means you

need twenty five independent planets per
property that you're trying to evaluate.

That quickly becomes pretty
tedious got to overlay and

find the sweet spot
that's pretty pretty and.

Fact of way of doing this.

So what we want to do was
visualize this in a different way

it should be able to handle the coming
to the problems should be easy to do and

should be universal in the application.

So here's an example you've got
seven components in three properties

that means we need seventy five plots from
the make sure we do the regression and

then plot them.

That's a lot of plots you
take the same problem.

Some components.

Three properties and you translate into
this classroom space then it's one plot.

Because you no longer represent
the properties inside the turn or

a diagram what you represent in there
are each of the pure components.

So it's a lot easier and
lower dimensionality to represent this.

Plus.

If you add another component you don't add
twenty five more plus you add another dot.

Now if you need more than three properties

then you need a multidimensional
representation which doesn't work.

However you can salvage mathematically
still a hell of a lot easier

set of equations of nonlinear
terms than you can trying to solve

the four non linear expressions they
get from regressing the D.O.B. problem.

So that was basically
what we came up with.

So I'll show you a quick
example of this and

I got to give my student
Charley credit for this.

He's an avid sailor and whenever he can
get out of the lab he wants to race.

So that the very first problem he wanted
to solve was optimize a polymer blend for

use in rep for sailboats OK so
that's what he did and the two scales that

we're dealing with here is the consumer
attributes and the molecular design.

So we put a lot of this out of Cornell
spoke on design of experiments.

So that was not a strength of yarn was one
property thready delegation was another

and then we said the third ability
probably is related in some shape or form.

Through the middle of all you.

Whether or not that's true or
not we don't know but

we had to do something about something
as intangible as float ability and

we didn't want to waste Charlie's time
by sending it out on the lake and

throwing different polymers in the water
so we came up with some values for

the properties targets and we had some
candidates of polymers that we could

put in just a simple that
came out of Cornell spoke.

Now this is how it was
done including this book.

So he had these eighteen response
surface plots for them to every.

When you did it in our method.

You had one plot and
this is a blow above it.

Because they're all clustered pretty
close together no pun intended.

This is the shape model which is one of
the ways that you can use a regression

the shape model does not center
anything whereas the Cox

model does now and
the shape model it looks like.

The component right here which is number

three should be pretty close
to being used directly as

a as a main component in
our eye of our brand.

But when you translate it to the Cox
model where everything is center around

a standard.

What happens is that the relative distance
from the standard indicates the strength

of the response how much effect a given
component has on the overall response.

So that means in this case the number
three has virtually no response.

No impact on the response so
it should be used as a filler.

So you can increase the clarity in just
these two plots which would be very hard

to get out of these eighteen in any
one look so that was kind of the.

Kind of the point of this whether or not.

Charlie actually has
made the polymer blend or

he just went to the bow store and bought.

A rope I don't.

No.

OK.

I'm sure this is just
a quick two minute version.

This is some of the record that
we're doing on more structure.

Problems.

Mr structured products we use
in a study from Sweden where

they're trying to design compressible
acetaminophen tablets and

so they have a variety of different
ingredients they can put in there

and we want to sell this
in a more efficient way.

Basically So these are the the properties
that they use angle repros compressibility

and water content they have a different
set of exceptions available and

they already derived all the mixing rules
for so that was easy to translate force.

What happens is when you regress
all this data you end up sometimes

with negative core fissions which when
we initially found related all the.

All the mass.

We didn't take into account.

So everything used to fit.

Inside this triangle.

Now all of a sudden we get a negative
core fissions because that's what

happens when you just run the regression.

So we didn't really know what that meant.

Except when we started to study the actual
responses it meant that the further

away you were it actually indicated
the strength of the effect.

So really the main component that has
an effect on this design is number six.

So when you blow it up.

Number six this summer up on
the fourth fifth or something.

But you'll notice that in all
the possible formulations that you can

help with it would have to be there and
that matches exactly what the experiment

was found out when they did that kind
of trial by a trial and error approach.

So the one thing that
we're struggling with.

What happens if we need new molecules
right now we're linking the attributes.

Chooser components.

We can do that without worrying
about the coming toward explosion.

But if we need new molecules
that aren't in the training said

what do we do about that.

Also when you have any secondary call in
the area or even very nasty non-linearity

in the regressions How do you have
a rat one way of doing that is to

use subspace subspace mappings
generally using latent variable models.

And I'm not going to spend
any time on that but

there's my student Charlie has
developed this and it was published.

Late last year I think and
I need to research.

But basically it allows you to.

Use design experiments and or P.L.S.
to come up with that your

property relationships and then you use
principal component now is to come up with

which other principal properties and
then there's some I say she steps and

you can use to determine the structure
of the of the final product but

I will skip that if you
concluding comments but

I've tried to show you is that
plastering method provides at least

a framework that allows you to
solve these probably driven

problems without having to commit to
components until the very last step.

It enables visualization that makes it.

Interesting from
a dimensionality perspective.

We can map attribute
data down to a subspace

I didn't show you that in detail with
some a thought in a linear functions

that means that you can guarantee
global optimality when you're solving.

That's definitely a plus.

Where are we going to know we need to
expand the general property descriptions

those of you who are doing operations
research and maybe hide high level

math of may have come across the concepts
of basis expansion base expansion is a.

A mathematical tool that
might provide is a way of

deriving the linearized expressions for
the operator functions.

We're working on integrating more
typological indices one of them is for

group contribution based Roshi design.

Which is a cool way of
structuring across the seas.

And so that you generate
a property from the flow sheet and

at the same time you generate
the proposition want to molecules to have.

Press or working on including
microstructure information particular

recruit there are many and so on and
a lot of that is coming from.

Professor Darby's group at Santa Barbara.

And basically we're looking at a variety
of ontology methods as well for

doing network analysis and so on.

So I had to acknowledge the funding from
National Science Foundation and from

the consortium the fossil fuel science and
although I get to do all the talking and

I'm the one that treated to the nice
dinner and the nice breakfast and lunch.

The work really good credit goes to
trial solver someone who was the main

one who worked on this and
the response I got developing

I've worked on pronouncing that for
three years but I finally got it.

And John does all the molecular
there's nine work that I presented.

So they're the ones that
really deserve the credit.

All right thank you very much.

And.

I really like.

This.

Why are you.

Well you need things.

You can see that we were.

Yes I like it.

That it's

not being a polymer expert I'm probably
going to jam my jam my foot in my mouth on

that one but I'll try what we really
want is to be able to describe either

the effect of the processing on the final
properties of the molecules let's say.

You know that a certain processing step

changes the glass
transmission temperature.

In this manner.

If you know that then you can use that
information either as a discrete point per

you know level of processing or it becomes
a pathway on the process side right.

At the same time you can map the
corresponding molecules or fragments of

molecules that you're trying to combine
until they basically hit the same point.

So you can you can solve both
at the same time you can target.

The.

The amount of processing that you
want to do to get the property target

you want the product to have or
vice versa.

The product of the property becomes
the interface between the two.

So you can either design a timer and

say OK this is the properties that
it has now in terms of doing that.

That's the normal way.

So there's no gain really of
doing it the way we're proposing.

But you could visually at least it
would it would be attractive you design

the molecule that provides
a certain point in space and

if you had a directory that is a function
of the processing whether to intersect is

the amount of processing you
would have to do to get there but

you would normally come from the process
side not the molecular side that.

You.

Yes yes yes.

So you're going to you're going to have a.

I would you call it you would have a.

Forgiven molecule that was
processed in the same way but

in two different extents
you would have a or

locus of points that would represent
the resulting final molecule.

Let me sense.

Now that means if you go to
a multi-processing steps that are vastly

different in fact on the properties it
becomes a more highly dimensional problem

but being represented in a linear way.

The only part we have to do with
nonlinearities is the final step.

We have to back calculate
the final property so

you should still be able to solve it
easier than as a full on brute force

makes them as an honest living
up to my station problem.

Yes

yes.

Sure.

We've actually taken the visual approach
and turn it into an algorithmic one.

It's very easy to do since
everything is linear and

you can set up the optimization
criteria pretty straightforward.

So we've we've really had limited for
two or

three properties only when
we want to do it visually.

We've also run a couple of examples where
we have properties that are functions or

multiple properties and

use that as a way of handling additional
non-linearity it is also possible.

We've done that with visually and
for that as a break.

Approach the hardest part
is not really a particular

type of property that is
harder than another one.

It really depends on how much data.

We can you get from first principles to do
the the transformation into a linearized

description whether or
not we have decent predictive power.

So there's the ones that
are hard to do at least from a.

From the molecular design
standpoint other ones that are very

different from what can be predicted
from group contribution methods or

from let's say tautological
indices methods.

The structural information like for
different kinds of functional nano

composites stuff like that is difficult
to do without it being data driven.

Where you're like yes.

You know.

You go back to you know all of that base

work there will be no.

Most room and Yes yes.

Let me give you the.

I said to the prediction
person's answer first and

then let me give you the truthful one.

OK.

The prediction person one says the
predictions are usually strong regardless

of whether it's one class of
properties one class of components or

another since they're all pretty similar
straight simple see six to see eight.

Hydrocarbons with one functional group.

It shouldn't be very different.

In terms of the quality of the properties.

The reality is whether or not they
actually perform like that with only three

properties to describe the mixing and
the behavior is questionable.

But it might be we took the example for

that purpose there that when they were
three very different properties but

the reality is you would have to test them
all or test the ones that at least fell

inside the feasible space
now that the point to make

really is not that we're not trying
to solve everything in one shot.

I don't believe and.

The optimization approach to go for
the brass ring in one shot.

I think the way to approach these kinds
of problems for exactly the reason you

point out is to generate all
the alternatives that are feasible.

And then pick the best one.

Now the ones that are infeasible the ones
that would be screened out by what we did

those would never work whether or
not the ones we did finally work.

We're not sure but
there are candidates there one is a didn't

satisfy the first criteria
we set up will never work.

So at least we've limited the search space
in this case to three that show promise.

The other eleven or the other eight that
were screened out they would never work

because they would not satisfy
the initial constraints whether or

not the three that we did were
satisfy every constraint.

I don't know but
the other eight would definitely not show.

You.

Most of it from data.

So it's I regret.

You know you know.

I like the ones that we've used so

far we actually haven't done the ones
that I showed today we haven't you.

We haven't done the regression ourselves
we found those and other references.

But the work they were trying to do on
bases expansion as a as a method for do.

That you can pretty much it.

There's analogies there to doing systems
identification approaches we can fix

the structure so in bases expansion
you can fix what kind of for

Maj you want to do have and try to.

Fit the data to those kinds
of expressions and then

we're not limited if we use that approach
to let's say polynomial functions or

anything like that we can set in
my power we want as long as we can

come up with that linear mixing
of the non-linear terms.

That's all we need.

But the ones that we do so
far we haven't really.

Derived ourselves the work that I was

that I mentioned very briefly
on the P.L.S. P.C.A. work.

The regression core fission
is there are one way of

you know coming up with these kinds of.

Of expressions.

Now you don't know depending
on how you set up the POS in

the P.C.A. you may not be
able to at least in standard

software be able to hide functional
descriptions in the principal components.

So they may end up being the simple
linear by linear quadratic and so on but

then you could always rerun those and
try to repressurize those into a linear

form with non-linear terms that you.

And so I mean you know.

You know you can still use.

You know that the point is that once you
have descriptions of the properties.

They're no longer process specific
some of them might be like the plan or

processing would be probably specific but
you can probably.

Generate enough of those
descriptions at some point you know

to be able to represent.

Let's say a class of problems
that relate to palm or

processing because there's a certain
effect on polymers of a certain size or

morphology that this process will have
on its properties and once we have that

kind of information available then
it becomes you know generalizable.

Thank you.

You can still use.