DynaDiff uses weight-graph diffusion with a functional consistency loss and dynamics-informed prompting to generate adapted predictors, reporting 10.78% average accuracy gains over baselines while amortizing adaptation cost offline.
Learning Dynamical Systems from Partial Observations
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abstract
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled by an unknown time-varying differential equation, and the evolution term is estimated from the data, using a neural network. Any future state can then be computed by placing the associated differential equation in an ODE solver. We first evaluate our approach on shallow water and Euler simulations. We find that our method not only demonstrates high quality long-term forecasts, but also learns to produce hidden states closely resembling the true states of the system, without direct supervision on the latter. Additional experiments conducted on challenging, state of the art ocean simulations further validate our findings, while exhibiting notable improvements over classical baselines.
representative citing papers
A feed-forward parameter-to-latent mapping plus a parameter-conditioned Neural ODE decouples space, time, and PDE parameters in a single physics-informed surrogate.
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Generative Adaptation of Dynamics to Environmental Shifts via Weight-space Diffusion
DynaDiff uses weight-graph diffusion with a functional consistency loss and dynamics-informed prompting to generate adapted predictors, reporting 10.78% average accuracy gains over baselines while amortizing adaptation cost offline.
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Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs
A feed-forward parameter-to-latent mapping plus a parameter-conditioned Neural ODE decouples space, time, and PDE parameters in a single physics-informed surrogate.