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In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
Parameter estimation for dynamical systems remains challenging due to non-convexity and sensitivity to initial parameter guesses. Recent deep learning approaches enable accurate and fast parameter estimation but do not exploit transferable…
Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…
In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…
As one of the triumphs and milestones of robust statistics, Huber regression plays an important role in robust inference and estimation. It has also been finding a great variety of applications in machine learning. In a parametric setup, it…
Traditional fault diagnosis methods struggle to handle fault data, with complex data characteristics such as high dimensions and large noise. Deep learning is a promising solution, which typically works well only when labeled fault data are…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal…
Neural networks are powerful tools in various applications, and quantifying their uncertainty is crucial for reliable decision-making. In the deep learning field, the uncertainties are usually categorized into aleatoric (data) and epistemic…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…
This paper investigates the stability of deep ReLU neural networks for nonparametric regression under the assumption that the noise has only a finite p-th moment. We unveil how the optimal rate of convergence depends on p, the degree of…
We propose a novel approach for loss reserving based on deep neural networks. The approach allows for joint modeling of paid losses and claims outstanding, and incorporation of heterogeneous inputs. We validate the models on loss reserving…
This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot…
Characterization of quantum objects, being them states, processes, or measurements, complemented by previous knowledge about them is a valuable approach, especially as it leads to routine procedures for real-life components. To this end,…
Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this…
The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However,…
We present a class of algorithms capable of directly training deep neural networks with respect to large families of task-specific performance measures such as the F-measure and the Kullback-Leibler divergence that are structured and…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…