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Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…

Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…

Stochastic partial differential equations (SPDEs) describe the evolution of random processes over space and time, but their solutions are often analytically intractable and computationally expensive to estimate. In this paper, we propose…

It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…

The prevailing of artificial intelligence-of-things calls for higher energy-efficient edge computing paradigms, such as neuromorphic agents leveraging brain-inspired spiking neural network (SNN) models based on spatiotemporally sparse…

How to improve generative modeling by better exploiting spatial regularities and coherence in images? We introduce a novel neural network for building image generators (decoders) and apply it to variational autoencoders (VAEs). In our…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…

Predictive learning uses a known state to generate a future state over a period of time. It is a challenging task to predict spatiotemporal sequence because the spatiotemporal sequence varies both in time and space. The mainstream method is…

We introduce Flexi-VAE, a data-driven framework for efficient single-shot forecasting of nonlinear parametric partial differential equations (PDEs), eliminating the need for iterative time-stepping while maintaining high accuracy and…

We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…

Spiking Neural Networks (SNNs) provide a promising framework for energy-efficient and biologically grounded computation; however, scalable learning in deep recurrent architectures with sparse connectivity remains a major challenge. In this…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Short-term load forecasting (STLF) is challenging due to complex time series (TS) which express three seasonal patterns and a nonlinear trend. This paper proposes a novel hybrid hierarchical deep learning model that deals with multiple…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

We propose Lite-STGNN, a lightweight spatial-temporal graph neural network for long-term multivariate forecasting that integrates decomposition-based temporal modeling with learnable sparse graph structure. The temporal module applies…

We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…