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Uncertainty Quantification-enabled inversion of nuclear responses�with SciDAC NUCLEI

Scientific Achievement

Developed physics-driven deep learning model for accurately retrieving electroweak response functions from imaginary-time correlation functions with uncertainty quantification.

Significance and Impact

Solved a notoriously ill-posed problem with uncertainty quantification
Enable diffusion Monte Carlo calculation of lepton-nucleus scattering of larger nuclei than currently possible.

Technical Approach

Construct physics-informed basis function to efficiently capture the essential feature of nuclear responses (Ent-NN).
Propagate the uncertainty in the imaginary-time correlators into the reconstructed responses (UQ-NN)
To noisier input Euclidean responses correspond wider uncertainty bands (in green).
Favorable comparison with existing conventional (MaxEnt) and deep learning approaches (PhysNN).

PI(s)/Facility Lead(s): Krishnan Raghavan, Alessandro Lovato

Collaborating Institutions: Argonne National Laboratory

ASCR Program: Scidac Rapids-Nuclei partnership.

ASCR PM: Kalyan Perumala

Publication(s) for this work: https://doi.org/10.48550/arXiv.2310.18756

Figure: (top left) EntNN and UQ-NN reconstructions of one peak responses; (top right) EntNN and UQ-NN reconstructions of two peak responses; (bottom) UQNN estimate of uncertainty for different sigma (experimental error estimate).

Estimating response functions for large nuclei is hard because large uncertainties introduce errors into Maximum entropy calculations (the standard method). With UQNN, we can perform calculation for such large nuclei and moreover provide an estimate of uncertainty that is proportional to the errors in the scattering experiments.

LOCAL LAB POC: Krishnan Raghavan (MCS), Alessandro Lovato

TALKING POINTS:

Quantum Monte Carlo is commonly used for computer simulations in physics, chemistry, biology, and materials science and extracting the electroweak response for a Helium proton is an inverse problem that is ill-posed with large uncertainty that must be quantified.
To obviate this, we build a computationally inexpensive surrogate model that utilizes a basis function specifically derived from physics and performs better than the traditional MaxEnt approach and provides uncertainty estimates that are missing in the traditional approaches as seen from table
Not only better performance, but, the developed UQ-NN model provides uncertainty estimates that are proportional to the noise from the Quantum Monte Carlo simulations.

METADATA:

Name of the associated awarded project:

PI name(s): Krishnan Raghavan, Alessandro Lovato

Name of the program: Scidac – Rapids and Nuclei partnership.

CITATIONS:

Work under review with Physical Review C (second revision)

�https://doi.org/10.48550/arXiv.2310.18756