Error-Conditioned Neural Solvers

arXiv:2606.27354 · cs.LG, cs.AI, cs.CV, cs.NA, math.NA · Submitted 2026-06-25 · Read on arXiv

cs.LG, cs.AI, cs.CV, cs.NA, math.NA

Submitted: 2026-06-25

Updated: 2026-10-12

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• PDE residual — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Distribution Shift — 1× in this paper · explained in 9 episodes
• Surrogate Model — 1× in this paper · explained in 3 episodes
• Surrogate Models — 1× in this paper · explained in 2 episodes

Sources

• VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models
• Fourier Neural Operator for Parametric Partial Differential Equations
• GenCast: Diffusion-based ensemble forecasting for medium-range weather
• Palette: Image-to-Image Diffusion Models
• PRISMA: Improving the Accuracy-Latency Frontier of Diffusion-based PDE Solvers Using Physics-Informed Spectral Attention
• Score-Based Generative Modeling through Stochastic Differential Equations
• Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints
• Crystal Diffusion Variational Autoencoder for Periodic Material Generation

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