Related papers: Inverse Optimization Without Inverse Optimization:…
Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a…
Many real-world problems can be naturally described by mathematical formulas. The task of finding formulas from a set of observed inputs and outputs is called symbolic regression. Recently, neural networks have been applied to symbolic…
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…
Inverse optimization involves inferring unknown parameters of an optimization problem from known solutions and is widely used in fields such as transportation, power systems, and healthcare. We study the contextual inverse optimization…
The transformer architecture has demonstrated remarkable capabilities in modern artificial intelligence, among which the capability of implicitly learning an internal model during inference time is widely believed to play a key role in the…
Many decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. Recently, problems in this class have been successfully addressed via end-to-end learning…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
Discovering new physical products and processes often demands enormous experimentation and expensive simulation. To design a new product with certain target characteristics, an extensive search is performed in the design space by trying out…
Determining whether a program terminates is a core challenge in program analysis with direct implications for correctness, verification, and security. We investigate whether transformer architectures can recognise termination patterns…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based…
Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…
We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…
In this paper, we consider the supervised pre-trained transformer for a class of sequential decision-making problems. The class of considered problems is a subset of the general formulation of reinforcement learning in that there is no…