Related papers: From Uniform to Adaptive: General Skip-Block Mecha…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

Spiking Neural Networks (SNNs) are promising biologically plausible models of computation which utilize a spiking binary activation function similar to that of biological neurons. SNNs are well positioned to process spatiotemporal data, and…

Spiking Neural Networks (SNNs) are one of the most promising bio-inspired neural networks models and have drawn increasing attention in recent years. The event-driven communication mechanism of SNNs allows for sparse and theoretically…

Simulation-based optimization (SO or SBO) has become increasingly important to address challenging transportation network design problems. In this paper, we propose to solve two toll pricing problems with different levels of complexity…

Transformers achieve state-of-the-art results across many tasks, but their uniform application of quadratic self-attention to every token at every layer makes them computationally expensive. We introduce DTRNet (Dynamic Token Routing…

Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying…

Direct training of Spiking Neural Networks (SNNs) on neuromorphic hardware can greatly reduce energy costs compared to GPU-based training. However, implementing Backpropagation (BP) on such hardware is challenging because forward and…

Safe memory reclamation (SMR) algorithms suffer from a trade-off between bounding unreclaimed memory and the speed of reclamation. Hazard pointer (HP) based algorithms bound unreclaimed memory at all times, but tend to be slower than other…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…

The problem of training spiking neural networks (SNNs) is a necessary precondition to understanding computations within the brain, a field still in its infancy. Previous work has shown that supervised learning in multi-layer SNNs enables…

Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random…

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…

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…

Spiking neural networks (SNNs) exhibit superior energy efficiency but suffer from limited performance. In this paper, we consider SNNs as ensembles of temporal subnetworks that share architectures and weights, and highlight a crucial issue…

The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as…

Neuromorphic computing and, in particular, spiking neural networks (SNNs) have become an attractive alternative to deep neural networks for a broad range of signal processing applications, processing static and/or temporal inputs from…

We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal…

Transformer models have achieved promising results on natural language processing (NLP) tasks including extractive question answering (QA). Common Transformer encoders used in NLP tasks process the hidden states of all input tokens in the…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a…