# Latent Twins

arXiv: https://arxiv.org/abs/2509.20615 · HTML: https://mlsanity.com/paper/2509.20615/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 89 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 30 of 32)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [On the Turing Completeness of Modern Neural Network Architectures](https://mlsanity.com/paper/1901.03429/) (2019)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder](https://mlsanity.com/paper/2308.05882/) (2023)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling](https://mlsanity.com/paper/2403.10748/) (2024)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Weak-Form Latent Space Dynamics Identification](https://mlsanity.com/paper/2311.12880/) (2023)
- [Towards a Robust Parameterization for Conditioning Facies Models Using Deep Variational Autoencoders and Ensemble Smoother](https://mlsanity.com/paper/1812.06900/) (2018)
- [Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilation](https://mlsanity.com/paper/2101.02121/) (2021)
- [Analog ensemble data assimilation and a method for constructing analogs with variational autoencoders](https://mlsanity.com/paper/2006.01101/) (2020)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [Efficient Training of Deep Neural Operator Networks via Randomized Sampling](https://mlsanity.com/paper/2409.13280/) (2024)
- [A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization](https://mlsanity.com/paper/2501.14636/) (2025)
- [Paired Wasserstein Autoencoders for Conditional Sampling](https://mlsanity.com/paper/2412.07586/) (2024)
- [Ensemble Kalman filter in latent space using a variational autoencoder pair](https://mlsanity.com/paper/2502.12987/) (2025)

## Built on by (most cited first, 3 of 3)

- [Latent Space Inference via Paired Autoencoders](https://mlsanity.com/paper/2601.11397/) (2026)
- [Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification](https://mlsanity.com/paper/2602.02948/) (2026)
- [Physics-conforming Latent Twins](https://mlsanity.com/paper/2606.15053/) (2026)

## Abstract (arXiv)

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 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.