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

Neural scaling laws establish a predictable relationship between model performance and data or compute, offering crucial guidance for resource allocation in new domains and tasks. Yet such laws are most needed precisely where they are…

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models…

Deep learning (DL) has become an essential tool in prognosis and health management (PHM), commonly used as a regression algorithm for the prognosis of a system's behavior. One particular metric of interest is the remaining useful life (RUL)…

Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…

In this work, we solve inverse problems of nonlinear Schr\"{o}dinger equations that can be formulated as a learning process of a special convolutional neural network. Instead of attempting to approximate functions in the inverse problems,…

Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce and the dimensionality is high. Although GPs are known for…

Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physics-informed neural networks fundamentally depart from this…

Catastrophic forgetting remains a fundamental challenge for neural networks when tasks are trained sequentially. In this work, we reformulate continual learning as a control problem where learning and preservation signals compete within…

We propose a general framework for neural network compression that is motivated by the Minimum Description Length (MDL) principle. For that we first derive an expression for the entropy of a neural network, which measures its complexity…

Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches…

This paper introduces the first, open source software library for Constraint Consistent Learning (CCL). It implements a family of data-driven methods that are capable of (i) learning state-independent and -dependent constraints, (ii)…

Conventional solvers are often computationally expensive for constrained optimization, particularly in large-scale and time-critical problems. While this leads to a growing interest in using neural networks (NNs) as fast optimal solution…

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…

We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…

When deploying machine learning solutions, they must satisfy multiple requirements beyond accuracy, such as fairness, robustness, or safety. These requirements are imposed during training either implicitly, using penalties, or explicitly,…

Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

Continual learning aims to emulate the human ability to continually accumulate knowledge over sequential tasks. The main challenge is to maintain performance on previously learned tasks after learning new tasks, i.e., to avoid catastrophic…

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be…

Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…