Related papers: Learning Under Laws: A Constraint-Projected Neural…

Recent work in scientific machine learning (SciML) has focused on incorporating partial differential equation (PDE) information into the learning process. Much of this work has focused on relatively "easy" PDE operators (e.g., elliptic and…

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data…

In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conservation laws, in particular the Euler systems. To predict a…

Regression is one of the core problems tackled in supervised learning. Rectified linear unit (ReLU) neural networks generate continuous and piecewise-linear (CPWL) mappings and are the state-of-the-art approach for solving regression…

We present a physics-constrained neural network (PCNN) approach to solving Maxwell's equations for the electromagnetic fields of intense relativistic charged particle beams. We create a 3D convolutional PCNN to map time-varying current and…

We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy…

Various natural language processing tasks are structured prediction problems where outputs are constructed with multiple interdependent decisions. Past work has shown that domain knowledge, framed as constraints over the output space, can…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

This paper presents a neural network filter method based on contraction operators to address model collapse in recursive training of generative models. Unlike \cite{xu2024probabilistic}, which requires superlinear sample growth…

Contrastive learning has emerged as a powerful method in deep learning, excelling at learning effective representations through contrasting samples from different distributions. However, neural collapse, where embeddings converge into a…

We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear…

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…

Continual learning is the ability to acquire new knowledge without forgetting the previously learned one, assuming no further access to past training data. Neural network approximators trained with gradient descent are known to fail in this…

Running faster will only get you so far -- it is generally advisable to first understand where the roads lead, then get a car ... The renaissance of machine learning (ML) and deep learning (DL) over the last decade is accompanied by an…

We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear…

Real-world training data is often noisy; for example, human annotators assign conflicting class labels to the same instances. Partial-label learning (PLL) is a weakly supervised learning paradigm that allows training classifiers in this…

Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in…