[2508.05190] Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference

Computer Science > Machine Learning arXiv:2508.05190 (cs) [Submitted on 7 Aug 2025 (v1), last revised 27 Feb 2026 (this version, v3)] Title:Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference Authors:Luis Mandl, Dibyajyoti Nayak, Tim Ricken, Somdatta Goswami View a PDF of the paper titled Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference, by Luis Mandl and Dibyajyoti Nayak and Tim Ricken and Somdatta Goswami View PDF HTML (experimental) Abstract:Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire trajectories in one pass, often fail to capture the causal dependencies and generalize poorly outside the training time horizon. Autoregressive (AR) approaches, evolving the system step by step, suffer from error accumulation, limiting long-term accuracy. These shortcomings limit the long-term accuracy and reliability of both strategies. To address these issues, we introduce the Physics-Informed Time-Integrated Deep Operator Network (PITI-DeepONet), a dual-output architecture trained via physics-informed or hybrid physics- and data-driven objectives to ensure stable, accurate long-term evolution well beyond the training horizon. Instead of forecasting future states, the networ...