Related papers: Structure-Preserving Operator Learning
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),…
Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…
Solving partial differential equations remains a central challenge in scientific machine learning. Neural operators offer a promising route by learning mappings between function spaces and enabling resolution-independent inference, yet they…
There is an increasing need of continual learning in dynamic systems, such as the self-driving vehicle, the surveillance drone, and the robotic system. Such a system requires learning from the data stream, training the model to preserve…
We develop an approach to growing deep network architectures over the course of training, driven by a principled combination of accuracy and sparsity objectives. Unlike existing pruning or architecture search techniques that operate on…
Learning under non-smooth objectives remains a fundamental challenge in machine learning, as abrupt changes in conditioning variables can induce highly non-smooth loss landscapes and destabilize optimization. This difficulty is particularly…
Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…
Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…
This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs)…
Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…
Learning with physical systems is an emerging paradigm that seeks to harness the intrinsic nonlinear dynamics of physical substrates for learning. The impetus for a paradigm shift in how hardware is used for computational intelligence stems…
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…
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…
Solving partial differential equations (PDEs) efficiently is essential for analyzing complex physical systems. Recent advancements in leveraging deep learning for solving PDE have shown significant promise. However, machine learning…
Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes.…
Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…
We introduce Small PDE U-Net Solver (SPUS), a compact and efficient foundation model (FM) designed as a unified neural operator for solving a wide range of partial differential equations (PDEs). Unlike existing state-of-the-art PDE…
Cloud robotics enables robots to offload high-dimensional motion planning and reasoning to remote servers. However, for continuous manipulation tasks requiring high-frequency control, network latency and jitter can severely destabilize the…
Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…
Traditional transfer learning typically reuses large pre-trained networks by freezing some of their weights and adding task-specific layers. While this approach is computationally efficient, it limits the model's ability to adapt to…