الملخص
We study the problem of recovering the governing ODE of a dynamical system from unstructured, high-dimensional observations such as images. Existing methods for ODE discovery typically assume direct measurements of the variables, or do not provide theoretical guarantees on the learned variables and equations. While Causal Representation Learning (CRL) methods provide guarantees on identifying variables from high-dimensional observations up to component-wise diffeomorphisms, we show that in general these variables cannot be used directly as input to equation discovery methods, which typically assume that the variables will lead to sparse equations. So we introduce SParse Equivalent Equation Discovery AutoEncoder (SPEED-AE), a framework that combines a pretrained CRL method with a component-wise autoencoder that learns transformations of variables that are amenable to sparse ODE discovery. We show that for polynomial ODEs, this additional step allows us to restrict the identifiability of each variable from polynomial to monomial diffeomorphisms. Experiments on Lotka-Volterra, Lorenz, and a two-pendulum system show that SPEED-AE improves on the disentanglement of the CRL methods and that it recovers ODEs that are closest to the ground truth, while achieving state-of-the-art forecasting performance.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Trenta, A., Massidda, R., Bacciu, D., & Magliacane, S. (2026). Identifying ODEs from Unstructured Data with Causal Representation Learning. https://omanscience.com/ar/articles/identifying-odes-from-unstructured-data-with-causal-representation-learning
MLA 9
Trenta, Alessandro, et al. "Identifying ODEs from Unstructured Data with Causal Representation Learning." https://omanscience.com/ar/articles/identifying-odes-from-unstructured-data-with-causal-representation-learning.
شيكاغو (المؤلف–التاريخ)
Trenta, Alessandro, Riccardo Massidda, Davide Bacciu, and Sara Magliacane. 2026. "Identifying ODEs from Unstructured Data with Causal Representation Learning." https://omanscience.com/ar/articles/identifying-odes-from-unstructured-data-with-causal-representation-learning.
هارفارد
Trenta, A., Massidda, R., Bacciu, D. and Magliacane, S. (2026) 'Identifying ODEs from Unstructured Data with Causal Representation Learning', Available at: https://omanscience.com/ar/articles/identifying-odes-from-unstructured-data-with-causal-representation-learning.
فانكوفر
Trenta A, Massidda R, Bacciu D, Magliacane S. Identifying ODEs from Unstructured Data with Causal Representation Learning. https://omanscience.com/ar/articles/identifying-odes-from-unstructured-data-with-causal-representation-learning
IEEE
A. Trenta, R. Massidda, D. Bacciu, and S. Magliacane, "Identifying ODEs from Unstructured Data with Causal Representation Learning," https://omanscience.com/ar/articles/identifying-odes-from-unstructured-data-with-causal-representation-learning.