Latent twin operator models evolving physical systems with flexible sensor data
Latent Twin Operator
Computational Engineering, Finance, and Science
Summary
Many real-world physical systems are monitored by sensors that can change their number and placement over time, making it hard to predict the system’s behavior with fixed methods. The authors propose the Latent Twin Operator, a machine learning model that learns a compact hidden representation of such systems and can evolve this representation directly over time between any moments. This model can handle varying numbers and locations of sensors and be queried at different resolutions without retraining. It performs well on various time-dependent physical equations and adapts to coarser data without losing accuracy.
What this means in practice
- •For sensor network operators: Predict time-evolving physical fields accurately even when sensor setups change over time or differ by deployment.
- •For computational fluid dynamics engineers: Improve longer-term predictions of fluid flow by evolving learned latent states instead of relying on repeated stepwise simulation.
Authors
Deepanshu Verma, Riley Chen, Matthias Chung
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.