Related papers: Generalized Lagrangian Neural Networks
Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural…
We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…
Graph neural networks (GNNs) have become compelling models designed to perform learning and inference on graph-structured data. However, little work has been done to understand the fundamental limitations of GNNs for scaling to larger…
Deep residual networks (ResNets) have shown state-of-the-art performance in various real-world applications. Recently, the ResNets model was reparameterized and interpreted as solutions to a continuous ordinary differential equation or…
The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…
The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are…
Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry. We demonstrate how L-CNNs can be…
Accelerating the solution of nonlinear partial differential equations (PDEs) while maintaining accuracy at coarse spatiotemporal resolution remains a key challenge in scientific computing. Physics-informed machine learning (ML) methods such…
This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…
The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with…
We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of…
Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…
The present project aims to use machine learning, specifically neural networks (NN), to learn the trajectories of a set of coupled ordinary differential equations (ODEs) and decrease compute times for obtaining ODE solutions by using this…
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
This review aims to conduct a comparative analysis of liquid neural networks (LNNs) and traditional recurrent neural networks (RNNs) and their variants, such as long short-term memory networks (LSTMs) and gated recurrent units (GRUs). The…
Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged at each…
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…
Neural ordinary differential equations (neural ODEs) are a popular type of deep learning model that operate with continuous-depth architectures. To assess how well such models perform on unseen data, it is crucial to understand their…
Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better…