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Non-Affinity and Beyond:
Towards Robust Uncertainty Quantification For Real-Time Nuclear Dynamics
Kyle Godbey
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Confluence of Opportunity
Credit: Colourful Nuclide Chart created by Ed Simpson
Also…
Superheavy element formation
Neutron-rich element formation
Multinucleon transfer reactions
Light-ion fusion
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On the Experimental Side
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Across Computing
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In traditional HPC
Cloud Compute
Quantum Computing
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And Through Interdisciplinary Collaborations
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Beyond these, industry partners in HPC, ML experts, applied mathematicians, statisticians, and computer scientists are all happy to collaborate
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Credit: Boehnlein, Amber, et al. Colloquium: Machine learning in nuclear physics. Rev. Mod. Phys. (2022) 94:031003.10.1103/RevModPhys.94.031003
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Menu
Brief Overview of:
Uncertainty Quantification
Emulators
Past and Present Progress
Intentions for the Future
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What I Mean By ‘UQ’
In short, theoretical models are imperfect.
But that’s fine, so long as we have a sense of how certain we are of any given prediction.
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What I Mean By ‘UQ’
The ultimate goal of robust calibration for theoretical models is a collection of reasonable parameters for that model, given a set of data it was informed with.
We can also explore those distributions after the fact for new predictions.
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How Can We Do ‘UQ’?
There are many ways! In this talk I will be referring to direct Bayesian calibration when discussing model calibration.
This amounts to using some sort of sampling technique to explore the posterior distribution of the model parameters to determine what is reasonable.
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How Can We Do ‘UQ’?
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Why Do ‘UQ’?
In short, models are more useful when they are:
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A Note On Cost
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Enter: Emulators
Keep in mind: When developing emulators you have to balance both your speed and accuracy budget for your particular use case
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Types of Emulators
Two large classes, but all aim to deliver predictions quickly. Ideally emulators can estimate emulation error as well.
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Model-driven (intrusive)
Reduced basis method
Data-driven (nonintrusive)
Neural networks
Gaussian process
Dynamic mode decomposition
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RBM Crash Course
Two important steps:
Training
Projecting
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Principal Component Analysis
Bonilla E, Giuliani P, Godbey K, Lee D, Training and projecting: A reduced basis method emulator for many-body physics. Phys Rev C (2022) 106:054322.doi:10.1103/PhysRevC.106.054322
where
Important! Space of small n is defined by your reduced basis
Space of big N is the original mesh size
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Applied to: Density Functional Theory
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Applied to: Density Functional Theory
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Credit: Schunck N, editor. Energy Density Functional Methods for Atomic Nuclei. Bristol: IoP Publishing; 2019
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Vanilla RBM Results
For a basis of 2 across the testing set,
RMSE = 5.9×10−3
Time-to-solution:
42.3 ms ± 2.87 ms (24~ samples/second)
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What’s limiting our sample rate in this case?
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How to Handle Non-Affinity?
Vintage Galerkin projection is great for affine dependence on your model parameters (and expansion coefficients), not so much when you can’t precompute terms.
A way around this, then, is to simply forget the origin of those terms:
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How to Handle Non-Affinity?
By expanding the non-affine terms with their own basis we can kick the can down the road, but we still need the coefficients.
To get at them, we can interpolate by doing the projection with δ’s:
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Where
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How to Handle Non-Affinity?
This works really well! For a similar basis size and accuracy performance, our time-to-solution gets dropped down to: 423.8 μs ± 44.5 μs (2300~ samples/second)
Our next steps on this front are to ensure the accuracy is maintained across the parameter space and that we achieve similar timings for larger nuclei
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Where to Next? Dynamics!
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With RBMs working so well for structure, the next logical step is to apply them to reactions and dynamics to enable large-scale UQ efforts
For scattering, there are a few additional considerations in applying the Galerkin projection, but overall it’s straightforward
The real challenge comes in extending this to time-dependent methods where t is now a parameter
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Real-time Dynamics
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Real-time Dynamics - Fusion
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K. Godbey, C Simenel, and A. S. Umar, Absence of hindrance in microscopic 12C + 12C fusion study, Phys. Rev. C 100, 024619 (2019)
Single fusion reaction:
One trajectory + Constraints
Few hours/single node
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Real-time Dynamics - Quasifission
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K. Godbey, A. S. Umar, and C. Simenel, “Deformed shell effects in 48Ca+249Bk quasifission fragments”, Phys. Rev. C 100, 024610 (2019).
Quasifission systematics:
100~ trajectories
Few days/multi-node
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Real-time Dynamics - Equilibration
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C. Simenel, K. Godbey, and A. S. Umar, Timescales of Quantum Equilibration, Dissipation and Fluctuation in Nuclear Collisions, Phys. Rev. Lett. 124, 212504 (2020)
Global Systematics:
1000~ trajectories
Few weeks/multi-node
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Approaching Real-Time Dynamics
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Thus far, all EDFs have been determined without input from reactions data, limiting the predictive power for certain phenomena
Fusion cross sections, for instance, are incredibly sensitive to static properties such as the deformation and neutron skin of the nucleus
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UQ of Fusion
Image Credit:
J. D. McDonnell, N. Schunck, D. Higdon, J. Sarich, S. M. Wild, and W. Nazarewicz, Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements, Phys. Rev. Lett.114, 122501 (2015).
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UQ of Fusion
K. Godbey, A. S. Umar, and C. Simenel, “Theoretical uncertainty quantification for heavy-ion fusion”, Phys. Rev. C 106, L051602 (2022) (Editor’s Suggestion).
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40Ca + 40Ca
48Ca + 48Ca
K. Godbey, A. S. Umar, and C. Simenel, “Theoretical uncertainty quantification for heavy-ion fusion”, Phys. Rev. C 106, L051602 (2022) (Editor’s Suggestion).
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48Ca + 48Ca
K. Godbey, A. S. Umar, and C. Simenel, “Theoretical uncertainty quantification for heavy-ion fusion”, Phys. Rev. C 106, L051602 (2022) (Editor’s Suggestion).
48Ca + 48Ca
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Hurdles to Clear
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To include such data in calibration efforts would require a massive reduction in evaluation time for any Bayesian approaches
Asking an emulator to reproduce all the preceding videos for any given time is a tall order, so our current direction is to pursue data-driven approaches
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Approaching Real-Time Dynamics
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Two methods are currently being explored to learn the nonlinear dynamics of TDDFT:
Neural implicit flow
Fourier neural operator
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, A. Anandkumar, “Fourier Neural Operator for Parametric Partial Differential Equations”, ICLR Proceedings (2021).
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Approaching Real-Time Dynamics
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Even with efficient emulators, it’s possible that direct Bayesian calibration is out of reach for time-dependent problems.
ML-based emulators like NIF will still be extremely important as deployable emulators for systematic/global studies, however.
Tools like polynomial chaos expansion may mitigates the need for 1,000,000s of evaluations of your surrogate model, however, bringing calibration back on the menu
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Bringing It All Together
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What, then, is the dream of a person with ultra-fast emulators and a deluge of experimental data on exotic nuclei?
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Bringing It All Together
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Link up to that pipeline of data and build a framework that can continuously calibrate models and make the tools for prediction and calibration widely accessible and usable
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Bringing It All Together
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The place to start is to rigorously quantify and mix our model predictions and present them in an easy to understand manner
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Bringing It All Together
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Deployed RBM Emulator
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Bringing It All Together
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Potential energy surface emulators for fission properties
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Bringing It All Together
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Future plans include real-time emulation of time-dependent problems
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Bringing It All Together
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While optimistic, the current environment necessitates a combination of dreaming big and capitalizing on our past developments
An easy way to accelerate this is to make it as simple as possible to get involved in applying the philosophy of UQ and machinery of efficient emulation
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Plugs and Promotions
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Introduction to Reduced-Basis Methods in Nuclear Physics
Online tutorial resource (always accepting contributions!)
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Plugs and Promotions
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FRIB-TA Summer School: Practical Uncertainty Quantification and Emulator Development in Nuclear Physics
June 26-28, 2023
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Immense Gratitude to All Collaborators!
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Funding
DOE NNSA Grant Nos. DE-NA0004074, DE-NA0003885
DOE Grant No. DE-SC0013365
Computing Resources
Australian National Computational Infrastructure Raijin and Gadi
Oak Ridge Leadership Computing Facility Summit
Argonne Leadership Computing Facility Polaris
Texas A&M High Performance Research Computing Terra and Ada
Michigan State University HPCC
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Background - Density Constraint + TDDFT
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Perform standard time evolution to time t and internuclear separation R and save the density
Start a static iteration to minimize the energy using the density from the time-dependent calculation at t and R
The converged energy is to then be interpreted as the static collective energy, EDC
Background - Density Constraint + TDDFT
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The potential is obtained by subtracting the static binding energies of the incoming fragments from EDC
V(R) = EDC - EA1 - EA2
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K. Godbey, A. S. Umar, and C. Simenel, “Theoretical uncertainty quantification for heavy-ion fusion”, Phys. Rev. C 106, L051602 (2022) (Editor’s Suggestion).
48Ca + 48Ca
Rskin = [0.13,0.22]
(range depends on model parameters)
Primary source of model uncertainty lies in the static description of the collision partners!
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Vanilla RBM Results
Time-to-solution:
42.3 ms ± 2.87 ms
Faster, but not quite there!
What’s the hold up?
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