giulianp@frib.msu.edu
Pablo Giuliani
Beyond projections:
Learning Equations from Data
Other brands
Dimensionality
reduction
ASCSN
Outline
2
My current MOR perspective
Reduced Coordinates and Reduced Equations
Ask questions
Equations from data
Gain and Pain
Questions and Challenges for our field
What’s out there?
Our approaches
Conclusions
Conclusions
2
1) I believe we could streamline the creation of reduced order models for nuclear physics
Structure
Astrophysics
Symmetries
Applications
Th.
Exp.
2) I believe mastering “learning equations from data” is going to be key
3) I believe we should invest in thermalizing with the state of the art of model order reduction
How it works
4
Parameters:
Density Functional Theory
How it works
5
Parameters:
Density Functional Theory
(Binding Energy)
How it works
6
Density Functional Theory
Parameters:
(Binding Energy)
.
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.
.
.
.
~5000 variables
High Fidelity
How it works
7
Density Functional Theory
Parameters:
(Binding Energy)
.
.
.
.
.
.
~5000 variables
~50 variables
Reduced
Model
High Fidelity
How it works
8
Density Functional Theory
Parameters:
(Binding Energy)
.
.
.
.
.
.
~5000 variables
~50 variables
Reduced Model
High Fidelity
Reduced
Model
High Fidelity
CAT plot
How it works
“High Fidelity”
“Emulated”
Physical model
Posterior distribution
Gaussian Process
Neural Networks
Model Order Reduction:
Variational Bayes
Chaos expansion
Normalizing flows
Reduced basis methods
(~eigenvector continuation)
Dynamic Mode Decomposition
SINDy and NIF
…
…
…
How it works
10
1) Find good reduced coordinates
2) Find equations for them
Reducing your model in two easy steps:
How it works
11
1) Find good reduced coordinates
2) Find equations for them
Reducing your model in two easy steps:
How it works
12
3 translations
3 rotations
+
1) Find good reduced coordinates
2) Find equations for them
Reducing your model in two easy steps:
How it works
13
3 translations
3 rotations
+
1) Find good reduced coordinates
2) Find equations for them
Reducing your model in two easy steps:
How it works
Quantum Harmonic Oscillator
How it works
Quantum Harmonic Oscillator
How it works
Quantum Harmonic Oscillator
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How it works
Quantum Harmonic Oscillator
.
.
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Long vector
How it works
Quantum Harmonic Oscillator
Many Long vectors
Solution Manifold
How it works
Quantum Harmonic Oscillator
Solution Manifold
Reduced space
How it works
Quantum Harmonic Oscillator
.
.
.
Dimension
n
Solution Manifold
Reduced space
>>
(300)
(2)
How it works
Quantum Harmonic Oscillator
.
.
.
Dimension
n
Solution Manifold
Reduced space
>>
(300)
(2)
How it works
Quantum Harmonic Oscillator
Reduced Basis
PCA
How it works
Quantum Harmonic Oscillator
Reduced Basis
PCA
How it works
Quantum Harmonic Oscillator
Reduced Basis
PCA
Boris Galerkin
How it works
Quantum Harmonic Oscillator
Reduced Basis
PCA
Boris Galerkin
Two coefficients
Two equations
How it works
Reducing your model in two easy steps:
2) Find equations for them
Reduced Basis Method
One equation per coefficient
Principal Component
Analysis
1) Find good reduced coordinates
Harmonic Oscillator Example
How it works
Reduced Basis Method
Linear Embedding
How it works
Reduced Basis Method
Linear Embedding
Good
Bad
PCA Doctor
Gain and Pain
Gain and Pain
Skyrme DFT
RMF DFT
Scattering
Time dynamics
AFDMC
Gain and Pain
31
Harmonic Oscillator Example
All is easy
Gain and Pain
32
Harmonic Oscillator Example
All is easy
33
Skyrme DFT
VERY non-linear
Harmonic Oscillator Example
All is easy
Gain and Pain
34
Skyrme DFT
VERY non-linear
Toy model:
Harmonic Oscillator Example
All is easy
Gain and Pain
Relativistic Mean Fields
Harmonic Oscillator Example
All is easy
Gain and Pain
Relativistic Mean Fields
Harmonic Oscillator Example
All is easy
Gain and Pain
Gain and Pain
Harmonic Oscillator Example
All is easy
Relativistic Mean Fields
Gain and Pain
Harmonic Oscillator Example
All is easy
Relativistic Mean Fields
Gain and Pain
Harmonic Oscillator Example
All is easy
Relativistic Mean Fields
Scattering
Harmonic Oscillator Example
All is easy
Gain and Pain
Scattering
Empirical Interpolation Method
Harmonic Oscillator Example
All is easy
Gain and Pain
Gain and Pain
Harmonic Oscillator Example
All is easy
Scattering
Empirical Interpolation Method
Two more “issues”
Harmonic Oscillator Example
All is easy
Experimental control
Singular Values
Components k
Two more “issues”
Harmonic Oscillator Example
All is easy
Experimental control
Singular Values
Components k
?
Two more “issues”
Harmonic Oscillator Example
All is easy
Extended Reduced Coordinates
Two more “issues”
Harmonic Oscillator Example
All is easy
Extended Reduced Coordinates
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Equations from Data
47
Our approaches
Equations from Data
48
Vintage Galerkin
Our approaches
Equations from Data
49
Vintage Galerkin
Our approaches
Equations from Data
50
Learn Equations from data
Fit from data
Vintage Galerkin
Black-box Galerkin
Our approaches
Equations from Data
51
Learn Equations from data
Fit from data
Vintage Galerkin
Black-box Galerkin
Our approaches
Closer to non-linear embedding
Equations from Data
52
Learn Equations from data
Fit from data
Vintage Galerkin
Black-box Galerkin
Danny Jammooa
Daniel Lee
Dean Lee
Patrick Cook
Morten Hjorth-Jensen
https://arxiv.org/abs/2401.11694
Fit from data
Equations from Data
53
Learn Equations from data
Fit from data
Vintage Galerkin
Black-box Galerkin
Danny Jammooa
Daniel Lee
Dean Lee
Patrick Cook
Morten Hjorth-Jensen
https://arxiv.org/abs/2401.11694
Very different application
Fit from data
Equations from Data
Inefficient
Our approaches
Equations from Data
55
Learn Equations from data
~ 3,000 faster than high fidelity
Inefficient
Our approaches
Edgard B.
Ruchi G.
Diogenes F.
Equations from Data
Our approaches
Casey
Ingo
Rahul
Stefano
Kyle
LANL team
Equations from Data
Equation
Of
State
Our approaches
Equations from Data
Equation
Of
State
Our approaches
Brendan Reed
Equations from Data
Equation
Of
State
Predictors
Our approaches
Brendan Reed
Brendan Reed
Brendan Reed
Equation
Of
State
Predictors
This is what I meant by inefficient
Our approaches
Equations from Data
Equations from Data
Equation
Of
State
Predictors
This is what I meant by inefficient
Our approaches
That’s how ROSE works!
Equations from Data
62
What’s out there?
Equations from Data
63
What’s out there?
Equations from Data
64
What’s out there?
Equations from Data
65
What’s out there?
A lot
Like, a lot a lot
Equations from Data
66
What’s out there?
A lot
Like, a lot a lot
Questions and challenges
67
What’s out there?
Questions and challenges
68
What’s out there?
Questions and challenges
69
What’s out there?
Awesome stuff we have done!
Questions and challenges
70
What’s out there?
MOR Technology from 2004
Awesome stuff we have done!
Questions and challenges
71
What’s out there?
Big part of my contribution to physics
MOR Technology from 2004
Questions and challenges
72
What’s out there?
Why these work?
Fit from data
PMM
Questions and challenges
73
What’s out there?
Why these work?
Fit from data
PMM
Right tool for the right job
Questions and challenges
74
What’s out there?
Why these work?
Fit from data
PMM
Right tool for the right job
Questions and challenges
75
What’s out there?
Why these work?
Fit from data
PMM
Right tool for the right job
Questions and challenges
76
What’s out there?
Why these work?
Fit from data
PMM
When and how they break?
Questions and challenges
77
What’s out there?
Why these work?
Fit from data
PMM
Casey
When and how they break?
Questions and challenges
78
What’s out there?
Why these work?
When and how they break?
What do we do from here?
Questions and challenges
79
What’s out there?
Why these work?
When and how they break?
What do we do from here?
ASCSN
Conclusions
2
1) I believe we could streamline the creation of reduced order models for nuclear physics
Structure
Astrophysics
Symmetries
Applications
Th.
Exp.
2) I believe mastering “learning equations from data” is going to be key
3) I believe we should invest in thermalizing with the state of the art of model order reduction
Further resources
81
Thank-yous
ASCSN Team
Jorge Piekarewicz
Frederi Viens
Kyle Godbey
Edgard Bonilla
Witek Nazarewicz
Dean Lee
Magda Kuich
Ana Posada
Moses Chan
Daniel Phillips
Eric Flynn
Daniel Odell
Daniel Lay
Filomena Nunes
Yanlai Chen
Aaron Phillip
Landon Buskirk
Dirac
Ruchi Garg
Ingo Twes
Kyle Beyer
Amy Anderson
And thank you,
for listening
People who pay
my lunch and collaborations
Diogenes Figueroa
Friends & collaborators
Manuel Catacora-Rios
Yukari Yamauchi
Dick Furnstahl
Ágnes Mócsy
Brendan Reed
Alexandra Semposki
…
http://databookuw.com/
https://dr.ascsn.net
Amy Lovell
https://forum.ascsn.net/t/about-the-2023-frib-ta-summer-school/42
Michelle Kuchera
Vojta Kejzlar
Ruoyu Cheng
Link to slides
Sudhanva Lalit
Megan Campbell
Chloe Hebborn
giulianp@
frib.msu.edu
Cassandra Armstrong
Rahul Somasundaram
Stefano Gandolf
Christian Drischler
Patrick Cook
Danny Jammooa