Related papers: NOFE - Neural Operator Function Embedding

Recently, Network Embedding (NE) has become one of the most attractive research topics in machine learning and data mining. NE approaches have achieved promising performance in various of graph mining tasks including link prediction and…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

The ability to reason about changes in the environment is crucial for robots operating over extended periods of time. Agents are expected to capture changes during operation so that actions can be followed to ensure a smooth progression of…

In high-dimensional and high-stakes contexts, ensuring both rigorous statistical guarantees and interpretability in feature extraction from complex tabular data remains a formidable challenge. Traditional methods such as Principal Component…

Embedding network data into a low-dimensional vector space has shown promising performance for many real-world applications, such as node classification and entity retrieval. However, most existing methods focused only on leveraging network…

We propose the Mixture of Frozen Experts (MoFE) architecture, which integrates Parameter-efficient Fine-tuning (PEFT) and the Mixture of Experts (MoE) architecture to enhance both training efficiency and model scalability. By freezing the…

We propose the Manifold Function Encoder (MFE) for identifying different functions defined on different manifolds. Both a manifold in Euclidean space and a function defined on this manifold can be viewed as bounded linear functionals on a…

Spiking Neural Networks (SNNs) offer significant potential for enabling energy-efficient intelligence at the edge. However, performing full SNN inference at the edge can be challenging due to the latency and energy constraints arising from…

Impressive advances in acquisition and sharing technologies have made the growth of multimedia collections and their applications almost unlimited. However, the opposite is true for the availability of labeled data, which is needed for…

Dimensionality reduction is essential in simulation-based shape design, where high-dimensional parameterizations hinder optimization, surrogate modeling, and systematic design-space exploration. Parametric Model Embedding (PME) addresses…

Understanding the relation between deep and shallow neural networks is extremely important for the theoretical study of deep learning. In this work, we discover an embedding principle in depth that loss landscape of an NN "contains" all…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon…

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined…

We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…

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…