Related papers: Learning Equations for Extrapolation and Control

During the last few years, significant attention has been paid to the stochastic training of artificial neural networks, which is known as an effective regularization approach that helps improve the generalization capability of trained…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

The prediction of salient areas in images has been traditionally addressed with hand-crafted features based on neuroscience principles. This paper, however, addresses the problem with a completely data-driven approach by training a…

In this article, we propose a data-enabled economic predictive control method for a class of nonlinear systems, which aims to optimize the economic operational performance while handling hard constraints on the system outputs. Two lifting…

Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to…

Deep neural networks tend to underestimate uncertainty and produce overly confident predictions. Recently proposed solutions, such as MC Dropout and SDENet, require complex training and/or auxiliary out-of-distribution data. We propose a…

In many machine learning applications, labeled data is scarce and obtaining more labels is expensive. We introduce a new approach to supervising neural networks by specifying constraints that should hold over the output space, rather than…

The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain…

Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…

We address a three-tier data-driven approach to solve the inverse problem in complex systems modelling from spatio-temporal data produced by microscopic simulators using machine learning. In the first step, we exploit manifold learning and…

We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control…

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…

We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a trainable neural network while preserving the conservative…

Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…

We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control.…

Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a number of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of…

Current deep neural networks (DNNs) can easily overfit to biased training data with corrupted labels or class imbalance. Sample re-weighting strategy is commonly used to alleviate this issue by designing a weighting function mapping from…

Artificial neural networks have been successfully applied to a variety of business application problems involving classification and regression. Although backpropagation neural networks generally predict better than decision trees do for…

We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of…

In this paper, we introduce an efficient backpropagation scheme for non-constrained implicit functions. These functions are parametrized by a set of learnable weights and may optionally depend on some input; making them perfectly suitable…