Conditioning on PDE Parameters to Generalise Deep Learning Emulation of Stochastic and Chaotic Dynamics

• URL: http://arxiv.org/abs/2509.09599v1
• Date: Thu, 11 Sep 2025 16:37:45 GMT
• Title: Conditioning on PDE Parameters to Generalise Deep Learning Emulation of Stochastic and Chaotic Dynamics
• Authors: Ira J. S. Shokar, Rich R. Kerswell, Peter H. Haynes,
• Abstract summary: We present a deep learning emulator for chaotic andtemporal-temporal systems conditioned on the parameter values of the underlying partial differential equations (Ps)<n>Our approach involves pre-training the model on a single parameter domain, followed by fine-tuning on a smaller, yet diverse dataset, enabling generalisation across a broad range of parameter values.<n>This enables computationally efficient pre-training on smaller domains while requiring only small additional dataset to learn how to generalise to larger domain sizes.
• Score: 0.1753733541634709
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on a single parameter domain, followed by fine-tuning on a smaller, yet diverse dataset, enabling generalisation across a broad range of parameter values. By incorporating local attention mechanisms, the network is capable of handling varying domain sizes and resolutions. This enables computationally efficient pre-training on smaller domains while requiring only a small additional dataset to learn how to generalise to larger domain sizes. We demonstrate the model's capabilities on the chaotic Kuramoto-Sivashinsky equation and stochastically-forced beta-plane turbulence, showcasing its ability to capture phenomena at interpolated parameter values. The emulator provides significant computational speed-ups over conventional numerical integration, facilitating efficient exploration of parameter space, while a probabilistic variant of the emulator provides uncertainty quantification, allowing for the statistical study of rare events.

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