Latent Twin Operator
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 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.
Related
- On the Riemann Hypothesis: A Complete Proof via the Twin Operator Method
- HiLNO: A Hierarchical Latent Neural Operator with Multi-Scale Supervision for PDEs on General Geometries
- An Energy-Based Conservative-Dissipative Latent Neural Evolution Operator for Magnetization Dynamics
- A Semigroup-Aware Kernel Neural Operator with Latent Exponential Integration for Forced PDEs
- The twisted twin of the Grigorchuk group
BibTeX
@misc{verma2026latent,
title = {{Latent Twin Operator}},
author = {Deepanshu Verma and Riley Chen and Matthias Chung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35531},
eprint = {2609.35531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35531},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Latent Twin Operator
AU - Deepanshu Verma
AU - Riley Chen
AU - Matthias Chung
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35531
UR - https://arxiv.org/abs/2609.35531
AB - 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 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.
ER -