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We introduce Wave-PDE Nets, a neural architecture whose elementary operation is a differentiable simulation of the second-order wave equation. Each layer propagates its hidden state as a continuous field through a medium with trainable…

Machine Learning · Computer Science 2025-10-07 Harshil Vejendla

Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting…

Machine Learning · Statistics 2026-03-27 Tianlin Yang , Hailiang Du , Louis Aslett

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

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

Machine Learning · Computer Science 2024-11-21 AmirPouya Hemmasian , Amir Barati Farimani

Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional…

Machine Learning · Computer Science 2025-08-04 Xiong Xiong , Zhuo Zhang , Rongchun Hu , Chen Gao , Zichen Deng

Neural operators for time-dependent PDEs face a structural tension: spectral architectures (FNO and descendants) inherit exponential rollout-error growth from their one-step Lipschitz constant, while hierarchical U-Net operators trade…

Machine Learning · Computer Science 2026-05-12 Enrique Hernández Noguera , Md Meftahul Ferdaus , Elias Ioup , Mahdi Abdelguerfi , Julian Simeonov

This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends…

Machine Learning · Computer Science 2026-04-02 Sandeep Kumar Samota , Reema Gupta , Snehashish Chakraverty

We present a simple neural rendering architecture that helps variational autoencoders (VAEs) learn disentangled representations. Instead of the deconvolutional network typically used in the decoder of VAEs, we tile (broadcast) the latent…

Machine Learning · Computer Science 2019-08-15 Nicholas Watters , Loic Matthey , Christopher P. Burgess , Alexander Lerchner

Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms:…

Machine Learning · Computer Science 2026-03-17 Dibyajyoti Nayak , Somdatta Goswami

Recent advancements in deep learning have led to the development of various models for long-term multivariate time-series forecasting (LMTF), many of which have shown promising results. Generally, the focus has been on…

Machine Learning · Computer Science 2024-02-28 Shiyi Qi , Zenglin Xu , Yiduo Li , Liangjian Wen , Qingsong Wen , Qifan Wang , Yuan Qi

Multivariate time-series (MTS) forecasting is a paramount and fundamental problem in many real-world applications. The core issue in MTS forecasting is how to effectively model complex spatial-temporal patterns. In this paper, we develop a…

Machine Learning · Computer Science 2024-02-16 Jinliang Deng , Xiusi Chen , Renhe Jiang , Du Yin , Yi Yang , Xuan Song , Ivor W. Tsang

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…

Amortized variational inference in latent-variable forecasters creates a deployment gap: the test-time encoder approximates a training-time optimization-refined latent, but without access to future targets. This gap introduces unnecessary…

Machine Learning · Computer Science 2026-02-17 Abhijit Gupta

Spatiotemporal (ST) learning has become a crucial technique to enable smart cities and sustainable urban development. Current ST learning models capture the heterogeneity via various spatial convolution and temporal evolution blocks.…

Machine Learning · Computer Science 2024-03-05 Zhengyang Zhou , Qihe Huang , Binwu Wang , Jianpeng Hou , Kuo Yang , Yuxuan Liang , Yang Wang

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge…

Machine Learning · Computer Science 2026-05-20 Zinuo You , Jin Zheng , John Cartlidge

Accurate long-horizon prediction of spatiotemporal fields on complex geometries is a fundamental challenge in scientific machine learning, with applications such as additive manufacturing where temperature histories govern defect formation…

Machine Learning · Computer Science 2026-02-23 Lionel Salesses , Larbi Arbaoui , Tariq Benamara , Arnaud Francois , Caroline Sainvitu

Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…

Probability · Mathematics 2019-08-27 Christian Kuehn , Alexandra Neamtu

Spiking Neural Networks (SNNs) are a promising research direction for building power-efficient information processing systems, especially for temporal tasks such as speech recognition. In SNNs, delays refer to the time needed for one spike…

Neural and Evolutionary Computing · Computer Science 2024-08-13 Ilyass Hammouamri , Ismail Khalfaoui-Hassani , Timothée Masquelier

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

Machine Learning · Computer Science 2025-11-26 Yujin Kim , Sarah Dean

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

Machine Learning · Statistics 2025-03-04 Ziheng Guo , James Greene , Ming Zhong