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cs.LG2026
Loss Landscape Geometry of Partial Differential Equation Emulators: Or, Symmetry Learning via Gradient Alignment
James Amarel, Robyn Miller, Nicolas Hengartner +5
We study how neural emulators of partial differential equation solution operators internalize physical symmetries by introducing an influence-based diagnostic that measures the pro…
cs.LG2026
Towards Reasoning for PDE Foundation Models: A Reward-Model-Driven Inference-Time-Scaling Algorithm
Siddharth Mansingh, James Amarel, Ragib Arnab +10
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have…
cs.LG2024
Posterior Mean Matching: Generative Modeling through Online Bayesian Inference
Sebastian Salazar, Michal Kucer, Yixin Wang +2
This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model…