NeurIPS 2025

Hybrid Latent Representations for PDE Emulation
Ali Can Bekar
Helmholtz Centre Hereon
Geesthacht, Germany
ali.bekar@hereon.de
Siddhant Agarwal
Helmholtz Centre Hereon
Geesthacht, Germany
siddhant.agarwal@hereon.de
Christian Hüttig
Institute of Space Research
German Aerospace Center (DLR)
Berlin, Germany
christian.huettig@dlr.de
Nicola Tosi
Institute of Space Research
German Aerospace Center (DLR)
Berlin, Germany
nicola.tosi@dlr.de
David S. Greenberg
Helmholtz Centre Hereon
Geesthacht, Germany
david.greenberg@hereon.de
Abstract
For classical PDE solvers, adjusting the spatial resolution and time step offers
a trade-off between speed and accuracy. Neural emulators often achieve better
speed-accuracy trade-offs by operating on a compact representation of the PDE
system. Coarsened PDE fields are a simple and effective representation, but cannot
exploit fine spatial scales in the high-fidelity numerical solutions. Alternatively,
unstructured latent representations provide efficient autoregressive rollouts, but
cannot enforce local interactions or physical laws as inductive biases. To overcome
these limitations, we introduce hybrid representations that augment coarsened
PDE fields with spatially structured latent variables extracted from high-resolution
inputs. Hybrid representations provide efficient rollouts, can be trained on a simple
loss defined on coarsened PDE fields, and support hard physical constraints. When
predicting fine- and coarse-scale features across multiple PDE emulation tasks,
they outperform or match the speed-accuracy trade-offs of the best convolutional,
attentional, Fourier neural operator-based and autoencoding baselines.
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Introduction
Integrating partial differential equations (PDEs) can be computationally expensive, particularly for
chaotic and turbulent systems with fine-scale structures requiring high spatiotemporal resolution.
For traditional solvers, discarding fine-scale details reduces both cost and accuracy, but data-driven
emulators can...