Related papers: Neural Optimal Design of Experiment for Inverse Pr…

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…

This paper introduces a methodology designed to augment the inverse design optimization process in scenarios constrained by limited compute, through the strategic synergy of multi-fidelity evaluations, machine learning models, and…

Neural Ordinary Differential Equations (NODEs) probed the usage of numerical solvers to solve the differential equation characterized by a Neural Network (NN), therefore initiating a new paradigm of deep learning models with infinite depth.…

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…

Residual neural networks can be viewed as the forward Euler discretization of an Ordinary Differential Equation (ODE) with a unit time step. This has recently motivated researchers to explore other discretization approaches and train ODE…

High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…

Deep learning, as a highly efficient method for metasurface inverse design, commonly use simulation data to train deep neural networks (DNNs) that can map desired functionalities to proper metasurface designs. However, the assumptions and…

We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…

The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…

We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…

It is well known that the class of rotation invariant algorithms are suboptimal even for learning sparse linear problems when the number of examples is below the "dimension" of the problem. This class includes any gradient descent trained…

In this paper, we propose an iterative training algorithm for Neural ODEs that provides models resilient to control (parameter) disturbances. The method builds on our earlier work Tuning without Forgetting-and similarly introduces training…

Deep neural networks have shown impressive performance in supervised learning, enabled by their ability to fit well to the provided training data. However, their performance is largely dependent on the quality of the training data and often…

Recently, sparse training methods have started to be established as a de facto approach for training and inference efficiency in artificial neural networks. Yet, this efficiency is just in theory. In practice, everyone uses a binary mask to…

Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we…

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…

In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…