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Recently, deep generative models have been used for posterior inference in inverse problems, including high-stakes applications in medical imaging and scientific discovery, where the uncertainty of a prediction can matter as much as the…

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…

Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse…

Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to…

Both the backpropagation algorithm in machine learning and the maximum principle in optimal control theory are posed as a two-point boundary problem, resulting in a "forward-backward" lock. We derive a reformulation of the maximum principle…

We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but…

Predictive uncertainty estimation remains a challenging problem precluding the use of deep neural networks as subsystems within safety-critical applications. Aleatoric uncertainty is a component of predictive uncertainty that cannot be…

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Based on an analysis of the short range chemical environment of each atom in a system, standard machine learning based approaches to the construction of interatomic potentials aim at determining directly the central quantity which is the…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…

Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…

In this paper, we study the differentiability of implicitly defined functions which we encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild (Biometrika 84 (1997) 57-71; J. Statist. Plann.…

This paper proposes an Adaptive Learning Model Predictive Control strategy for uncertain constrained linear systems performing iterative tasks. The additive uncertainty is modeled as the sum of a bounded process noise and an unknown…

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

In this paper, we introduce a new method for applying the implicit function theorem to find nontrivial solutions to overdetermined problems with a fixed boundary (given) and a free boundary (to be determined). The novelty of this method…

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research…

Most estimators collapse all uncertainty modes into a single confidence score, preventing reliable reasoning about when to allocate more compute or adjust inference. We introduce Uncertainty-Guided Inference-Time Selection, a lightweight…

Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the dint of it feedforward networks can be used to solve or…

This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a…