Related papers: Learning Equations for Extrapolation and Control

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schr\"odinger equation, where the control variable…

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…

Neural networks reach state-of-the-art performance in a variety of learning tasks. However, a lack of understanding the decision making process yields to an appearance as black box. We address this and propose ConstraintNet, a neural…

Neural networks have proven to be effective at solving machine learning tasks but it is unclear whether they learn any relevant causal relationships, while their black-box nature makes it difficult for modellers to understand and debug…

Weakly-supervised learning is a paradigm for alleviating the scarcity of labeled data by leveraging lower-quality but larger-scale supervision signals. While existing work mainly focuses on utilizing a certain type of weak supervision, we…

We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were…

Many current autonomous systems are being designed with a strong reliance on black box predictions from deep neural networks (DNNs). However, DNNs tend to be overconfident in predictions on unseen data and can give unpredictable results for…

Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

Learning representations of well-trained neural network models holds the promise to provide an understanding of the inner workings of those models. However, previous work has either faced limitations when processing larger networks or was…

This paper studies continuous-time stochastic control problems whose controlled states are fully non-Markovian and depend on unknown model parameters. Such problems arise naturally in path-dependent stochastic differential equations,…

Composite-database micro-expression recognition is attracting increasing attention as it is more practical to real-world applications. Though the composite database provides more sample diversity for learning good representation models, the…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…

Large-scale pre-trained models have achieved remarkable success in many applications, but how to leverage them to improve the prediction reliability of downstream models is undesirably under-explored. Moreover, modern neural networks have…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Self-paced learning and hard example mining re-weight training instances to improve learning accuracy. This paper presents two improved alternatives based on lightweight estimates of sample uncertainty in stochastic gradient descent (SGD):…

We propose a custom learning algorithm for shallow over-parameterized neural networks, i.e., networks with single hidden layer having infinite width. The infinite width of the hidden layer serves as an abstraction for the…

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…