Context-aware diffusion models for solving partial differential equations

doi:10.1016/j.neunet.2026.109647

Context-aware diffusion models for solving partial differential equations

2026-09-17

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DOI：10.1016/j.neunet.2026.109647

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Abstract

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• We propose a context-aware diffusion-model-based framework for differential equation solving, formulating PDE solution learning as a guided denoising generation process. • A cross-attention-driven conditioning strategy is introduced to incorporate demonstration data and problem-specific conditions into each denoising step, enabling accurate and controllable solution generation. • Extensive experiments on linear, nonlinear, and variational differential equations show that the proposed method achieves competitive or superior solution accuracy compared with representative neural operator baselines, including FNO, DeepONet, ICON, OFormer, UNO, and GNO.

Keywords:

Diffusion model

Differential equation

Partial differential equations

Deep learning

Context-aware diffusion models for solving partial differential equations

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