Related papers: Latent Mamba Operator for Partial Differential Equ…

Partial differential equations (PDEs) are widely used to model complex physical systems, but solving them efficiently remains a significant challenge. Recently, Transformers have emerged as the preferred architecture for PDEs due to their…

Partial Differential Equations are foundational in modeling science and natural systems such as fluid dynamics and weather forecasting. The Latent Evolution of PDEs method is designed to address the computational intensity of classical and…

The neural operator (NO) framework has emerged as a powerful tool for solving partial differential equations (PDEs). Recent NOs are dominated by the Transformer architecture, which offers NOs the capability to capture long-range…

Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions. However, existing models, including recurrent neural…

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…

Probabilistic State Space Models (SSMs) are essential for Reinforcement Learning (RL) from high-dimensional, partial information as they provide concise representations for control. Yet, they lack the computational efficiency of their…

State space models (SSMs), such as Mamba, have emerged as an efficient alternative to transformers for long-context sequence modeling. However, despite their growing adoption, SSMs lack the interpretability tools that have been crucial for…

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…

Foundation models, now powering most of the exciting applications in deep learning, are almost universally based on the Transformer architecture and its core attention module. Many subquadratic-time architectures such as linear attention,…

Linear State Space Models (SSMs) offer remarkable performance gains in efficient sequence modeling, with constant inference-time computation and memory complexity. Recent advances, such as Mamba, further enhance SSMs with input-dependent…

Sequence modeling is a crucial area across various domains, including Natural Language Processing (NLP), speech recognition, time series forecasting, music generation, and bioinformatics. Recurrent Neural Networks (RNNs) and Long Short Term…

Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of…

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…

Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…

State Space Models (SSMs) have emerged as a promising alternative to Transformers for long-context sequence modeling, offering linear $O(N)$ computational complexity compared to the Transformer's quadratic $O(N^2)$ scaling. This paper…

Mamba has recently gained widespread attention as a backbone model for point cloud modeling, leveraging a state-space architecture that enables efficient global sequence modeling with linear complexity. However, its lack of local inductive…

Recent State Space Models (SSM), especially Mamba, have demonstrated impressive performance in visual modeling and possess superior model efficiency. However, the application of Mamba to visual tasks suffers inferior performance due to…

Human activity recognition (HAR) from inertial sensors is essential for ubiquitous computing, mobile health, and ambient intelligence. Conventional deep models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs),…

The Mamba layer offers an efficient selective state space model (SSM) that is highly effective in modeling multiple domains, including NLP, long-range sequence processing, and computer vision. Selective SSMs are viewed as dual models, in…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…