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Error-Conditioned Neural Solvers

techniqueactiveprovisionalerror-conditioned-neural-solvers-01da0427·1 events·first seen 3d ago

Aliases: Error-Conditioned Neural Solvers

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5arXiv · cs.AI·3d ago·source ↗

Error-Conditioned Neural Solvers (ENS) improve PDE surrogate accuracy by feeding residual fields as inputs

A new arXiv preprint introduces Error-Conditioned Neural Solvers (ENS), a method for neural PDE surrogates that passes the PDE residual field directly as input to the network at each iteration, enabling iterative self-correction rather than gradient-based residual minimization. The authors demonstrate theoretically and empirically that residual minimization is an unreliable proxy for reconstruction accuracy in ill-conditioned systems, explaining failures of prior hybrid methods. ENS achieves up to 10× accuracy gains on turbulent Kolmogorov flow across four PDE families, with lower compute cost than hybrid approaches and generalization under distribution shift including zero-shot cross-equation transfer.

Error-Conditioned Neural Solvers