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Reliability-based topology optimization (RBTO) requires repeated estimation of small failure probabilities and their gradients, making conventional nested Monte Carlo approaches computationally prohibitive for large scale structural…

Optimization and Control · Mathematics 2026-05-01 Maryam Maghazeh , Ayyappan Unnikrishna Pillai , Mohammad Masiur Rahaman , Subhayan De

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Numerical Analysis · Mathematics 2025-06-18 Matteo Caldana , Jan S. Hesthaven

We improve the accuracy of Guidance & Control Networks (G&CNETs), trained to represent the optimal control policies of a time-optimal transfer and a mass-optimal landing, respectively. In both cases we leverage the dynamics of the…

Machine Learning · Computer Science 2024-04-29 Sebastien Origer , Dario Izzo

Estimating average treatment effects from observational data is challenging under practical violations of the positivity assumption. Targeted Maximum Likelihood Estimators (TMLEs) are widely used because of their double robustness and…

Methodology · Statistics 2026-04-28 Yichen Xu , Susan Gruber , Mark J. van der Laan

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Machine Learning · Statistics 2022-06-20 Paidamoyo Chapfuwa , Sherri Rose , Lawrence Carin , Edward Meeds , Ricardo Henao

Accurate Travel Time Estimation (TTE) is critical for ride-hailing platforms, where errors directly impact user experience and operational efficiency. While existing production systems excel at holistic route-level dependency modeling, they…

Machine Learning · Computer Science 2026-01-07 Wenzhao Jiang , Jindong Han , Ruiqian Han , Hao Liu

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…

Machine Learning · Computer Science 2021-06-25 Zheng Fang , Qingqing Long , Guojie Song , Kunqing Xie

Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…

Machine Learning · Computer Science 2024-10-14 Matt L. Sampson , Peter Melchior

Traffic flow forecasting is a fundamental research issue for transportation planning and management, which serves as a canonical and typical example of spatial-temporal predictions. In recent years, Graph Neural Networks (GNNs) and…

Machine Learning · Computer Science 2024-02-27 Qingqing Long , Zheng Fang , Chen Fang , Chong Chen , Pengfei Wang , Yuanchun Zhou

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor…

Machine Learning · Computer Science 2023-02-09 Valerii Iakovlev , Cagatay Yildiz , Markus Heinonen , Harri Lähdesmäki

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

Machine Learning · Computer Science 2023-09-12 Katharina Ott , Prateek Katiyar , Philipp Hennig , Michael Tiemann

Does the use of auto-differentiation yield reasonable updates for deep neural networks (DNNs)? Specifically, when DNNs are designed to adhere to neural ODE architectures, can we trust the gradients provided by auto-differentiation? Through…

Machine Learning · Computer Science 2026-03-31 Yewei Xu , Shi Chen , Qin Li

This paper addresses imitation learning for motion prediction problem in autonomous driving, especially in multi-agent setting. Different from previous methods based on GAN, we present the conditional latent ordinary differential equation…

Robotics · Computer Science 2024-05-30 Khang Truong Giang , Yongjae Kim , Andrea Finazzi

We show that Neural ODEs, an emerging class of time-continuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based…

Machine Learning · Computer Science 2021-11-16 Sophie Gruenbacher , Ramin Hasani , Mathias Lechner , Jacek Cyranka , Scott A. Smolka , Radu Grosu

We propose a continuous neural network architecture, termed Explainable Tensorized Neural Ordinary Differential Equations (ETN-ODE), for multi-step time series prediction at arbitrary time points. Unlike the existing approaches, which…

Machine Learning · Computer Science 2022-07-13 Penglei Gao , Xi Yang , Rui Zhang , Kaizhu Huang

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Machine Learning · Computer Science 2024-05-07 Christina Runkel , Ander Biguri , Carola-Bibiane Schönlieb

The metro ridership prediction has always received extensive attention from governments and researchers. Recent works focus on designing complicated graph convolutional recurrent network architectures to capture spatial and temporal…

Machine Learning · Computer Science 2021-07-13 Chuyu Huang

This paper deals with the numerical integration of well-posed multiscale systems of ODEs or evolutionary PDEs. As these systems appear naturally in engineering problems, time-subcycling techniques are widely used every day to improve…

Analysis of PDEs · Mathematics 2015-10-07 Guillaume Dujardin , Pauline Lafitte

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

Numerical Analysis · Mathematics 2024-12-02 Nicola Farenga , Stefania Fresca , Simone Brivio , Andrea Manzoni

Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex…

Machine Learning · Computer Science 2024-08-14 Zibo Liu , Zhe Jiang , Shigang Chen