{"ID":2872277,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.09599","arxiv_id":"2509.09599","title":"Conditioning on PDE Parameters to Generalise Deep Learning Emulation of Stochastic and Chaotic Dynamics","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.","short_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 dat...","url_abs":"https://arxiv.org/abs/2509.09599","url_pdf":"https://arxiv.org/pdf/2509.09599v1","authors":"[\"Ira J. S. Shokar\",\"Rich R. Kerswell\",\"Peter H. Haynes\"]","published":"2025-09-11T16:37:45Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.DS\",\"nlin.CD\",\"physics.ao-ph\"]","methods":"[\"LoRA\"]","has_code":false}