Related papers: Merging Memory and Space: A State Space Neural Ope…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data…

Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps. We introduce Spectral Filtering Operator (SFO),…

Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional function spaces using conventional neural architectures, have…

Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with…

In this work, we introduce S4M, a new efficient speech separation framework based on neural state-space models (SSM). Motivated by linear time-invariant systems for sequence modeling, our SSM-based approach can efficiently model input…

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems…

Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to…

In recent years, Neural Operators(NO) have gradually emerged as a popular approach for solving Partial Differential Equations (PDEs). However, their application to large-scale engineering tasks suffers from significant computational…

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs)…

Data-driven techniques have emerged as a promising alternative to traditional numerical methods for solving PDEs. For time-dependent PDEs, many approaches are Markovian -- the evolution of the trained system only depends on the current…

We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…

State Space Models (SSMs) have emerged as a potent tool in sequence modeling tasks in recent years. These models approximate continuous systems using a set of basis functions and discretize them to handle input data, making them well-suited…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they…

The success of vision transformers-especially for generative modeling-is limited by the quadratic cost and weak spatial inductive bias of self-attention. We propose PDE-SSM, a spatial state-space block that replaces attention with a…

We study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous…

Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multi-stage process of…

Transformer models have achieved superior performance in various natural language processing tasks. However, the quadratic computational cost of the attention mechanism limits its practicality for long sequences. There are existing…

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…