相关论文: An attention-based neural ordinary differential eq…

Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials which utilize such properties is to precisely…

Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory…

Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we…

In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of…

We introduce Wave-PDE Nets, a neural architecture whose elementary operation is a differentiable simulation of the second-order wave equation. Each layer propagates its hidden state as a continuous field through a medium with trainable…

Dynamic signed networks (DSNs) are common in online platforms, where time-stamped positive and negative relations evolve over time. A core task in DSNs is dynamic edge prediction, which forecasts future relations by jointly modeling edge…

Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent,…

Transformers are state-of-the-art deep learning models that are composed of stacked attention and point-wise, fully connected layers designed for handling sequential data. Transformers are not only ubiquitous throughout Natural Language…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…

Vision Transformers (ViTs) have achieved state-of-the-art performance in image classification, yet their attention mechanisms often remain opaque and exhibit dense, non-structured behaviors. In this work, we adapt our previously proposed…

Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a…

Despite substantial progress in deep learning approaches to time-series reconstruction, no existing methods are designed to uncover local activities with minute signal strength due to their negligible contribution to the optimization loss.…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

Stability evaluation of black-box grid-tied inverters is vital for grid reliability, yet identification techniques are both data-hungry and blocked by proprietary internals. {To solve this, this letter proposes a latent-feature-informed…

In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…

A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…

A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on…