Latent Twins

• URL: http://arxiv.org/abs/2509.20615v1
• Date: Wed, 24 Sep 2025 23:43:19 GMT
• Title: Latent Twins
• Authors: Matthias Chung, Deepanshu Verma, Max Collins, Amit N. Subrahmanya, Varuni Katti Sastry, Vishwas Rao,
• Abstract summary: We propose a unifying framework that creates a hidden surrogate in latent space for the underlying equations.<n>Latent Twins mirror mathematical systems in a learned latent space governed by operators.
• Score: 0.3078691410268859
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical PDEs, dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With \emph{Latent Twins}, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ODEs and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with DeepONet and forecasts with a 4D-Var baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.

Related papers

• Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs [15.38864225184245]
  Inverse problems are the task of calibrating models to match data.<n>We develop a principled methodology for leveraging data from collections of distinct yet related physical systems.<n>We learn the shared unknown dynamics in the form of an ML-based closure model.
  arXiv  Detail & Related papers  (2026-03-04T10:30:08Z)
• Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations [65.80144621950981]
  We build on Wiener chaos expansions (WCE) to design neural operator (NO) architectures for SPDEs and SDEs.<n>We show that WCE-based neural operators provide a practical and scalable way to learn SDE/SPDE solution operators.
  arXiv  Detail & Related papers  (2026-01-03T00:59:25Z)
• Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models [6.403678133359229]
  latent dynamics in high-dimensional recordings are often characterized by a much smaller set of effective variables.<n>Most machine learning approaches tackle these tasks jointly by training autoencoders together with models that enforce dynamical consistency.<n>We propose to decouple the two problems by leveraging the recently introduced Foundation Inference Models (FIMs)<n>A proof of concept on a double-well system with semicircle diffusion, embedded into synthetic video data, illustrates the potential of this approach for fast and reusable coarse-graining pipelines.
  arXiv  Detail & Related papers  (2025-10-14T15:17:23Z)
• Enabling Local Neural Operators to perform Equation-Free System-Level Analysis [1.2468700211588881]
  Neural Operators (NOs) provide a powerful framework for computations involving physical laws.<n>We propose and implement a framework that integrates (local) NOs with advanced iterative numerical methods in the Krylov subspace.<n>We illustrate our framework via three nonlinear PDE benchmarks.
  arXiv  Detail & Related papers  (2025-05-05T01:17:18Z)
• Differentiable DG with Neural Operator Source Term Correction [0.0]
  We introduce an end-to-end differentiable framework for solving the compressible Navier-Stokes equations.<n>This integrated approach combines a differentiable discontinuous Galerkin solver with a neural network source term.<n>We demonstrate the performance of the proposed framework through two examples.
  arXiv  Detail & Related papers  (2023-10-29T04:26:23Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Solving High-Dimensional PDEs with Latent Spectral Models [74.1011309005488]
  We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space. LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks.
  arXiv  Detail & Related papers  (2023-01-30T04:58:40Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems [0.0]
  Two approaches for updating the digital twin are proposed. In both cases, the resulting expressions of updated digital twins are identical. The proposed approaches provide an exact and explainable description of the perturbations in digital twin models.
  arXiv  Detail & Related papers  (2022-12-19T04:25:59Z)
• Distributed Bayesian Learning of Dynamic States [65.7870637855531]
  The proposed algorithm is a distributed Bayesian filtering task for finite-state hidden Markov models. It can be used for sequential state estimation, as well as for modeling opinion formation over social networks under dynamic environments.
  arXiv  Detail & Related papers  (2022-12-05T19:40:17Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• Long-time integration of parametric evolution equations with physics-informed DeepONets [0.0]
  We introduce an effective framework for learning infinite-dimensional operators that map random initial conditions to associated PDE solutions within a short time interval. Global long-time predictions across a range of initial conditions can be then obtained by iteratively evaluating the trained model. This introduces a new approach to temporal domain decomposition that is shown to be effective in performing accurate long-time simulations.
  arXiv  Detail & Related papers  (2021-06-09T20:46:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.