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Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps…

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…

Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling…

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem. However, the most popular inference algorithms for SBL become too expensive for high-dimensional settings, due to the need to store and compute a…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust…

Spiking neural networks (SNNs) provide an energy-efficient solution by utilizing the spike-based and sparse nature of biological systems. Since the advent of Transformers, SNNs have struggled to compete with artificial networks on long…

Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the…

Spiking Neural Networks (SNNs) offer a biologically inspired computational paradigm, enabling energy-efficient data processing through spike-based information transmission. Despite notable advancements in hardware for SNNs, spike encoding…

We explore the hypothesis that poor compositional generalization in neural networks is caused by difficulties with learning effective routing. To solve this problem, we propose the concept of block-operations, which is based on splitting…

Sparse Mixture-of-Experts (SMoE) has gained prominence as a scalable and computationally efficient architecture, enabling significant growth in model capacity without incurring additional inference costs. However, existing SMoE models often…

We present MegaBlocks, a system for efficient Mixture-of-Experts (MoE) training on GPUs. Our system is motivated by the limitations of current frameworks, which restrict the dynamic routing in MoE layers to satisfy the constraints of…

Rendering is critical in fields like 3D modeling, AR/VR, and autonomous driving, where high-quality, real-time output is essential. Point-based neural rendering (PBNR) offers a photorealistic and efficient alternative to conventional…

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…

Energy efficient mobility management is an important problem in modern wireless networks with heterogeneous cell sizes and increased nodes densities. We show that optimization-based mobility protocols cannot achieve long-term optimal energy…

Adopting large-scale AI models in enterprise information systems is often hindered by high training costs and long development cycles, posing a significant managerial challenge. The standard end-to-end backpropagation (BP) algorithm is a…