Reduced Basis Method and Active Learning Emulate Proton-Deuteron Scattering, Reducing Computational Costs

Understanding the forces between protons and deuterons presents a fundamental challenge in nuclear physics, crucial for refining theoretical models of nuclear interactions. Alex Gnech from Old Dominion University and Jefferson Lab, alongside Xilin Zhang from Facility for Rare Isotope Beams at Michigan State University, and Christian Drischler from Ohio University, lead a team that has developed a new approach to tackle this problem. They present a computationally efficient method for simulating proton-deuteron scattering, utilising the Reduced Basis Method and active learning techniques to overcome the prohibitive costs of traditional high-fidelity calculations. This advancement significantly accelerates the process of calibrating theoretical models, such as chiral effective field theory, and promises to unlock more accurate predictions of nuclear behaviour, with potential applications extending to neutron-deuteron scattering and other complex nuclear systems. The team demonstrates remarkable accuracy, achieving emulation errors of less than one percent with minimal training data, paving the way for efficient Bayesian analysis of nuclear forces.

Nuclear Scattering, Few-Body Systems, and Computation

This compilation of research demonstrates a deep engagement with the theoretical and computational challenges of nuclear physics, scattering theory, and related fields. The references span decades, revealing a thorough understanding of the field’s historical development and current frontiers. A central theme is the application of computational methods, including Python libraries like SciPy and NumPy, to solve complex problems in nuclear physics. Researchers consistently explore effective field theories, which simplify complex nuclear interactions to make calculations more manageable, demonstrating a commitment to both theoretical rigor and practical computational techniques.

Reduced Basis Emulators for Nuclear Scattering

Scientists have developed a new methodology to accelerate calculations in nuclear physics, specifically for proton-deuteron scattering, a crucial process for refining our understanding of the forces between protons, neutrons, and deuterons. This innovation addresses a significant challenge in exploring the vast parameter space of chiral effective field theory, essential for accurately modeling nuclear forces. The study involved a detailed implementation of high-fidelity calculations, forming the foundation for constructing three distinct emulators.

These emulators leverage the similarities between solutions at different parameter settings, dramatically reducing computational costs without compromising accuracy. Researchers implemented variational and Galerkin-projection-based scattering emulators, enabling efficient predictions for scattering observables. To further optimize the process, they employed greedy algorithms as an active learning tool, strategically selecting optimal training points within the parameter space. Experiments demonstrate the exceptional performance of these emulators, achieving remarkably low emulation errors with a minimal number of training points, allowing for efficient calibration of chiral effective field theory nucleon interactions using Bayesian statistics. This methodology extends beyond proton-deuteron scattering, offering a versatile framework applicable to other nuclear scattering processes and finite quantum systems, paving the way for more comprehensive uncertainty quantification in nuclear physics calculations.

Reduced Basis Accelerates Nuclear Force Calculations

Scientists have developed a new method to significantly accelerate calculations in nuclear physics, specifically for understanding the forces between nucleons, protons and neutrons. This work focuses on nucleon-deuteron scattering, a crucial process for refining theoretical models of nuclear forces known as chiral effective field theory. The researchers demonstrated the effectiveness of an active learning strategy, termed “greedy”, to select the most informative parameter points for training the emulator, ensuring calculations are focused where they will yield the greatest improvement in accuracy.

The results show that relative emulation errors can be reduced to less than 1% using fewer than 10 high-fidelity training calculations in a two-dimensional parameter space, representing a substantial improvement in efficiency. The emulators accurately predict scattering amplitudes, enabling rapid exploration of the parameter space of nuclear forces. This method utilizes a linear approximation to the solution of the scattering equations, projecting the problem onto a lower-dimensional subspace to reduce computational cost while preserving the underlying physics. By exploiting similarities between solutions at different parameter settings, these emulators significantly reduce the computational burden while maintaining accuracy. The team successfully applied this approach to proton-deuteron scattering, utilizing two different nucleon forces and two scattering channels, paving the way for more efficient calibration of chiral effective field theory interactions and enabling researchers to explore a wider range of parameters and improve the precision of nuclear force models. While the current study focused on proton-deuteron scattering, extending the method to neutron-deuteron scattering is straightforward, and the approach could be further refined to address more complex parameter dependencies and applied to other nuclear scattering processes and finite systems.