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Stochastic first-order methods for empirical risk minimization employ gradient approximations based on sampled data in lieu of exact gradients. Such constructions introduce noise into the learning dynamics, which can be corrected through…

Continuous high frequency water quality monitoring is becoming a critical task to support water management. Despite the advancements in sensor technologies, certain variables cannot be easily and/or economically monitored in-situ and in…

Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

Determining, understanding, and predicting the so-called structure-property relation is an important task in many scientific disciplines, such as chemistry, biology, meteorology, physics, engineering, and materials science. Structure refers…

Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which…

We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by advection-dominated partial differential equations. Those systems have slow-decaying Kolmogorov n-width that…

Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

It has been observed that machine learning algorithms exhibit biased predictions against certain population groups. To mitigate such bias while achieving comparable accuracy, a promising approach is to introduce surrogate functions of the…

The ongoing development of quantum processors is driving breakthroughs in scientific discovery. Despite this progress, the formidable cost of fabricating large-scale quantum processors means they will remain rare for the foreseeable future,…

We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the…

The increasing use of stochastic models for describing complex phenomena warrants surrogate models that capture the reference model characteristics at a fraction of the computational cost, foregoing potentially expensive Monte Carlo…

We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…

We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

We present a detailed study of top-$k$ classification, the task of predicting the $k$ most probable classes for an input, extending beyond single-class prediction. We demonstrate that several prevalent surrogate loss functions in…

We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common…