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A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie…

Machine Learning · Computer Science 2020-07-01 Georgia Koppe , Hazem Toutounji , Peter Kirsch , Stefanie Lis , Daniel Durstewitz

Data-driven modeling of constrained multibody dynamics remains challenged by (i) the training cost of Neural ODEs, which typically require backpropagation through an ODE solver, and (ii) error accumulation in rollout predictions. We…

Machine Learning · Computer Science 2026-03-23 Hongyu Wang , Jingquan Wang , Dan Negrut

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

Numerical Analysis · Mathematics 2021-09-07 Ricardo A. Delgadillo , Jingwei Hu , Haizhao Yang

The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational…

Machine Learning · Statistics 2019-06-04 Wei Chen , Hythem Sidky , Andrew L Ferguson

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

Machine Learning · Computer Science 2025-05-28 Avik Pal , Alan Edelman , Christopher Rackauckas

Networked dynamic systems are ubiquitous in various domains, such as industrial processes, social networks, and biological systems. These systems produce high-dimensional data that reflect the complex interactions among the network nodes…

Systems and Control · Electrical Eng. & Systems 2023-10-02 Jiaxin Yu , Yanfang Mo , S. Joe Qin

In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…

Machine Learning · Computer Science 2017-06-05 Pratik Chaudhari , Adam Oberman , Stanley Osher , Stefano Soatto , Guillaume Carlier

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…

Numerical Analysis · Mathematics 2019-08-30 Benjamin Peherstorfer

Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While L\'evy processes provide a natural mathematical framework for…

Machine Learning · Computer Science 2026-05-12 Yaman Kindap , Manfred Opper , Benjamin Dupuis , Umut Simsekli , Tolga Birdal

Learning representations of underlying environmental dynamics from partial observations is a critical challenge in machine learning. In the context of Partially Observable Markov Decision Processes (POMDPs), state representations are often…

Machine Learning · Computer Science 2024-11-13 Chao Han , Debabrota Basu , Michael Mangan , Eleni Vasilaki , Aditya Gilra

The high cost of acquiring labels is one of the main challenges in deploying supervised machine learning algorithms. Active learning is a promising approach to control the learning process and address the difficulties of data labeling by…

Machine Learning · Computer Science 2019-11-19 Farhad Pourkamali-Anaraki , Michael B. Wakin

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works…

Machine Learning · Computer Science 2024-11-05 Wenjie Mei , Dongzhe Zheng , Shihua Li

Variational Autoencoders (VAEs) have become a popular approach for dimensionality reduction. However, despite their ability to identify latent low-dimensional structures embedded within high-dimensional data, these latent representations…

Machine Learning · Statistics 2020-08-27 Kaspar Märtens , Christopher Yau

Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn…

Numerical Analysis · Mathematics 2024-02-06 P. D. Hinds , M. V. Tretyakov

Trajectory forecasting is crucial for video surveillance analytics, as it enables the anticipation of future movements for a set of agents, e.g. basketball players engaged in intricate interactions with long-term intentions. Deep generative…

Computer Vision and Pattern Recognition · Computer Science 2024-08-30 Riccardo Benaglia , Angelo Porrello , Pietro Buzzega , Simone Calderara , Rita Cucchiara

Soft robots offer unmatched adaptability and safety in unstructured environments, yet their compliant, high-dimensional, and nonlinear dynamics make modeling for control notoriously difficult. Existing data-driven approaches often fail to…

Robotics · Computer Science 2025-11-03 Hehui Zheng , Bhavya Sukhija , Chenhao Li , Klemens Iten , Andreas Krause , Robert K. Katzschmann

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…

Machine Learning · Computer Science 2025-08-07 Yifei Zong , Alexandre M. Tartakovsky

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Computational Physics · Physics 2020-06-25 Jaime Lopez Garcia , Angel Rivero Jimenez