Related papers: Optimization-Informed Neural Networks
Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional…
We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…
In the field of Continual Learning, the objective is to learn several tasks one after the other without access to the data from previous tasks. Several solutions have been proposed to tackle this problem but they usually assume that the…
Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…
Learning the optimized solution as a function of environmental parameters is effective in solving numerical optimization in real time for time-sensitive applications. Existing works of learning to optimize train deep neural networks (DNN)…
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…
Physics-Informed Neural Networks have shown unique utility in parameterising the solution of a well-defined partial differential equation using automatic differentiation and residual losses. Though they provide theoretical guarantees of…
To shift the computational burden from real-time to offline in delay-critical power systems applications, recent works entertain the idea of using a deep neural network (DNN) to predict the solutions of the AC optimal power flow (AC-OPF)…
Leveraging machine learning to facilitate the optimization process is an emerging field that holds the promise to bypass the fundamental computational bottleneck caused by classic iterative solvers in critical applications requiring…
The energy management problem in the context of smart grids is inherently complex due to the interdependencies among diverse system components. Although Reinforcement Learning (RL) has been proposed for solving Optimal Power Flow (OPF)…
In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…
The optimization of deep neural networks can be more challenging than traditional convex optimization problems due to the highly non-convex nature of the loss function, e.g. it can involve pathological landscapes such as saddle-surfaces…
Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NNs). However the intriguing approach of training NNs with MIP solvers is under-explored.…
Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning''…
Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of the most intensively studied frameworks is the physics-informed neural network (PINN). However, PINN often fails to optimize the…
Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…
This paper discusses an outer-approximation guided optimization method for constrained neural network inverse problems with rectified linear units. The constrained neural network inverse problems refer to an optimization problem to find the…
This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…
We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and indirect viewpoints for optimal control of PDEs, and then…
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…