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Abstract

Summary

We present a Physics-Informed Denoising Diffusion Probabilistic Model (PIDDPM) for super-resolution and surrogate modelling of time-dependent physical systems. PIDDPM is conditioned on a coarse-resolution input at the current timestep and high-resolution ground truth from the two preceding timesteps, with the aim of reconstructing fine-scale solutions consistent with the underlying dynamics. PIDDPM acts as a surrogate, approximating the behaviour of nonlinear PDEs such as the Allen-Cahn equation without requiring full numerical simulation. Physics-based penalties are incorporated into the loss function to penalise lack of consistency with the governing equations and boundary conditions, ensuring that the generated outputs remain physically plausible. Our results demonstrate that PIDDPM significantly improves perceptual and physical accuracy compared to baseline DDPM, achieving higher PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index Measure) while reducing MSE (Mean Squared Error) and MSGE (Mean Squared Gradient Error). The model’s ability to learn temporal evolution and spatial refinement makes it a scalable and physically grounded alternative to traditional solvers. PIDDPM shows strong potential for resolution enhancement, interpolation and predictive modelling in subsurface workflows, offering a data-driven approach to accelerate simulations and support efficient decision-making in geoscientific domains.

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2025-11-10
2026-02-16

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References

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/content/papers/10.3997/2214-4609.202576020
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Physics-Informed Diffusion Model for Super-Resolution and Surrogate Modelling of Time-Dependent Partial Differential Equations
Conference Proceedings 2025, 1 (2025); https://doi.org/10.3997/2214-4609.202576020
/content/papers/10.3997/2214-4609.202576020
/content/papers/10.3997/2214-4609.202576020
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