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Physics-based Deep Learning
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This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up and running quickly. Beyond traditional supervised learning, we dive into physical loss-constraints, differentiable simulations, diffusion-based approaches for probabilistic generative AI, as well as reinforcement learning and advanced neural network architectures. These foundations are paving the way for the next generation of scientific foundation models. We are living in an era of rapid transformation. These methods have the potential to redefine what's possible in computational science.
Forward citations
Cited by 5 Pith papers
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GyroSwin: 5D Surrogates for Gyrokinetic Plasma Turbulence Simulations
GyroSwin predicts 5D gyrokinetic plasma turbulence autoregressively, matching heat-flux and turbulence spectra of GKW simulations at a fraction of the cost.
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Differentiable Cardiac Electrophysiology Simulations for Dynamical State and Parameter Estimation
A differentiable solver for cardiac reaction-diffusion waves recovers hidden states and parameters of the Aliev-Panfilov model from sparse, surface-only, or noisy voltage observations, including two experimental monol...
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From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier
LLM formal provers must shift from competition solvers to research agents that handle open-ended, under-specified frontier mathematics under machine-checked rigor.
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Solver-Integrated Adversarial Attacking and Training of Neural Operators
Solver-integrated PGD attacks produce stronger adversarial examples for neural operators than dictionary-based attacks, and round-based retraining improves some out-of-distribution accuracy but with mixed, costly results.
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Governing Equation Discovery from Data Based on Differential Invariants
PDE discovery guided by symmetry can be done by building the SINDy library from the differential invariants of the PDE's symmetry group, which shrinks the search space and improves success rates.
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