PDE Surrogate Modeling

PDE: Partial Differential Equation

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Overview

PDE surrogate modeling studies how to approximate the mapping from physical conditions, geometry, and parameters to a PDE’s solution, reducing the cost of repeated simulations. Methods range from reduced-order models such as POD and latent dynamics to neural operators such as Fourier Neural Operators and DeepONets, as well as mesh-based graph networks, transformers, and generative models. Many approaches combine these learned models with physical structure, including conservation laws, symmetries, boundary conditions, and numerical solvers, to improve reliability and support inverse problems or design optimization. A central challenge is balancing speed with accuracy under new geometries or regimes, stable long rollouts, fine-scale fidelity, and calibrated uncertainty; whether a surrogate saves time overall depends on training and deployment costs as well as inference speed.

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331 papers50 papers in the last four weeks, up 72% on the four weeks before. 0.3% of all new papers.

Oct 29, 2024

A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator

Physics-based Earth system models (ESMs) are essential for attributing climate change and generating scenario projections, yet their reliance on high-resolution numerical integration makes multi-decadal experiments expensive. In parallel, deep learning has delivered strong gains in short-range weather forecasting; however, auto-regressive roll-outs can accumulate error and become unstable when extended to decade-scale climate emulation. We introduce A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator, aimed at stable multi-year emulation across heterogeneous climate models and grid resolutions. A-UTE is trained on various physics-based models at varying spatial resolutions to emulate temperature fields over a 10-year horizon. A-UTE formulates climate emulation as a forward-time stochastic dynamical system. We propose an auto-regressive ODE-SDE surrogate in which transport dynamics are constrained by an advection consistent ODE component, while a learned neural SDE term models coarse-grained variability and cross-model discrepancy at monthly resolution. We train A-UTE under negative log-likelihood objective for principled uncertainty estimates and probabilistic evaluation. Experiments across 20 climate models show that A-UTE improves long roll-out stability and accuracy relative to relevant baselines, advancing data-driven climate emulation with explicit physical structure and uncertainty-aware predictions.

Hira Saleem, Cormac Purcell, Steven Sherwood +1

University of New South Wales, Sydney, NSW, Australia

Climate EmulationNeural Surrogate ModelingPDE Surrogate ModelingProbabilistic ForecastingStochastic Differential Equations
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