Related papers: Flowers: A Warp Drive for Neural PDE Solvers

Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…

Generating new molecules is fundamental to advancing critical applications such as drug discovery and material synthesis. Flows can generate molecules effectively by inverting the encoding process, however, existing flow models either…

Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…

Flower pollination is an intriguing process in the natural world. Its evolutionary characteristics can be used to design new optimization algorithms. In this paper, we propose a new algorithm, namely, flower pollination algorithm, inspired…

We develop a novel data-driven framework as an alternative to dynamic flux balance analysis, bypassing the demand for deep domain knowledge and manual efforts to formulate the optimization problem. The proposed framework is end-to-end,…

We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…

The stability of optical vortex structures in turbulent environments is critical for their applications in optical communication, quantum information, and structured light technologies. Although topological invariants, such as crossings and…

For the application of MPC design in on-line regulation or tracking control problems, several studies have attempted to develop an accurate model, and realize adequate uncertainty description of linear or non-linear plants of the processes.…

Spectral bias implies an imbalance in training dynamics, whereby high-frequency components may converge substantially more slowly than low-frequency ones. To alleviate this issue, we propose a cross-attention-based architecture that…

We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…

The recent success of multiple neural architectures like CNNs, Transformers, and MLP-Mixers motivated us to look for similarities and differences between them. We found that these architectures can be interpreted through the lens of a…

We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as…

Multi-head attention layers, as used in the Transformer neural sequence model, are a powerful alternative to RNNs for moving information across and between sequences. While training these layers is generally fast and simple, due to…

We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 3D block-structured collocated grids with distributed computational architectures. Our approach…

Training large language models (LLMs) requires substantial compute and energy. At the same time, renewable energy sources regularly produce more electricity than the grid can absorb, leading to curtailment, the deliberate reduction of clean…

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed…