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

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…

Physics-informed Neural Network (PINN) faces significant challenges when approximating solutions to conservation laws, particularly in ensuring conservation and accurately resolving discontinuities. To address these limitations, we propose…

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

As machine learning models, specifically neural networks, are becoming increasingly popular, there are concerns regarding their trustworthiness, specially in safety-critical applications, e.g. actions of an autonomous vehicle must be safe.…

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

Neural networks have demonstrated significant potential in solving partial differential equations (PDEs). While global approaches such as Physics-Informed Neural Networks (PINNs) offer promising capabilities, they often lack inherent…

In many applications, learning systems are required to process continuous non-stationary data streams. We study this problem in an online learning framework and propose an algorithm that can deal with adversarial time-varying and nonlinear…

When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…

Predictive learning ideally builds the world model of physical processes in one or more given environments. Typical setups assume that we can collect data from all environments at all times. In practice, however, different prediction tasks…

We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations…

Neural operators (NOs) have emerged as effective tools for modeling complex physical systems in scientific machine learning. In NOs, a central characteristic is to learn the governing physical laws directly from data. In contrast to other…

In the recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of PDEs is enforcing physical constraints and boundary conditions. In this work,…

Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…