A neural surrogate for the neutrino-matter coupling solve in a general-relativistic radiation-hydrodynamics code reaches parity at best because the target block is only about 17% of runtime and gating defers 97 to 99% of cells back to the exact solver.
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
One of the most promising applications of machine learning (ML) in computational physics is to accelerate the solution of partial differential equations (PDEs). The key objective of ML-based PDE solvers is to output a sufficiently accurate solution faster than standard numerical methods, which are used as a baseline comparison. We first perform a systematic review of the ML-for-PDE solving literature. Of articles that use ML to solve a fluid-related PDE and claim to outperform a standard numerical method, we determine that 79% (60/76) compare to a weak baseline. Second, we find evidence that reporting biases, especially outcome reporting bias and publication bias, are widespread. We conclude that ML-for-PDE solving research is overoptimistic: weak baselines lead to overly positive results, while reporting biases lead to underreporting of negative results. To a large extent, these issues appear to be caused by factors similar to those of past reproducibility crises: researcher degrees of freedom and a bias towards positive results. We call for bottom-up cultural changes to minimize biased reporting as well as top-down structural reforms intended to reduce perverse incentives for doing so.
representative citing papers
NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
Side-by-side timing comparison finds BEM solves the scattering problem in ~0.01 s while PINN training takes ~100 s, but trained PINN evaluates interior points ~100x faster than BEM.
citing papers explorer
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When a neural surrogate cannot accelerate a solver: runtime share, closed-loop drift, and the economics of uncertainty gating in a stiff coupled simulation
A neural surrogate for the neutrino-matter coupling solve in a general-relativistic radiation-hydrodynamics code reaches parity at best because the target block is only about 17% of runtime and gating defers 97 to 99% of cells back to the exact solver.
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Neural equilibria for long-term prediction of nonlinear conservation laws
NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
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Benchmarking Physics-Informed Neural Networks and Boundary Elements Methods for Wave Scattering
Side-by-side timing comparison finds BEM solves the scattering problem in ~0.01 s while PINN training takes ~100 s, but trained PINN evaluates interior points ~100x faster than BEM.