Problem
Research questions and friction points this paper is trying to address.
surrogate models
sensor configurations
arbitrary resolution
time-evolving PDEs
latent evolution
Latent Twin Operator
🤖 AI Summary
This study addresses the challenges faced by surrogate models for physical systems, specifically varying sensor resolutions and the coupling between temporal evolution and observational discretization. To overcome these issues, this work proposes the Latent Twin Operator, built upon a ConvCNP architecture to process arbitrarily distributed sensor data, which achieves spatiotemporal decoupled prediction by learning evolution mappings in the latent space. Notably, this research derives the first explicit convergence rate for context discretization error, enabling seamless cross-resolution transfer under fixed parameters. Experiments on heat equation and Navier-Stokes benchmarks demonstrate significantly reduced long-horizon prediction errors, validating both the theoretical convergence guarantees and the practical effectiveness of the proposed method.
📝 Abstract
Surrogate models deployed on real physical systems rarely see data at fixed resolutions: sensor configurations vary across deployments and may evolve over time as sensing infrastructure changes. We introduce the Latent Twin Operator (LTO), a latent-space surrogate for time-evolving PDEs with a Convolutional Conditional Neural Process (ConvCNP)-style encoder and decoder that accepts a context set of $N$ sensor observations with arbitrary placement and can be queried at any resolution. A learned latent evolution map advances the encoded state directly between arbitrary time points, decoupling temporal evolution from the observation and query discretizations. We derive an explicit $\mathcal{O}(N^{-2/(3D)})$ rate for the context discretization error in spatial dimension $D$ under quasi-uniform refinement. We verify the predicted decay empirically on a 2D heat-equation benchmark. Across time-dependent PDE benchmarks, LTO achieves strong accuracy under one-step comparisons and transfers from native to coarser spatial resolutions with fixed parameters. On Navier--Stokes, its direct latent evolution further reduces error over longer prediction horizons relative to recursive evaluation.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Latent Twin Operator
Surrogate Model
Conditional Neural Process
Latent Evolution
Partial Differential Equations
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