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Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the…

Machine Learning · Computer Science 2025-09-29 Juan Diego Toscano , Daniel T. Chen , Vivek Oommen , Jérôme Darbon , George Em Karniadakis

Population balance equation (PBE) models have potential to automate many engineering processes with far-reaching implications. In the pharmaceutical sector, crystallization model-based design can contribute to shortening excessive drug…

Computational Engineering, Finance, and Science · Computer Science 2024-11-04 Mohammed Alsubeihi , Arthur Jessop , Ben Moseley , Cláudio P. Fonte , Ashwin Kumar Rajagopalan

The aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along DNA sequences. These events are modeled by a Hawkes process. The biological problem is actually complex…

Statistics Theory · Mathematics 2010-11-11 Patricia Reynaud-Bouret , Sophie Schbath

Large organizations have seamlessly incorporated data-driven decision making in their operations. However, as data volumes increase, expensive big data infrastructures are called to rescue. In this setting, analytics tasks become very…

Databases · Computer Science 2020-03-17 Fotis Savva , Christos Anagnostopoulos , Peter Triantafillou

High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with…

Optimization and Control · Mathematics 2021-06-08 Joseph E. Gaudio , Anuradha M. Annaswamy , José M. Moreu , Michael A. Bolender , Travis E. Gibson

We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…

Statistics Theory · Mathematics 2018-06-13 Dmitrii Ostrovskii , Zaid Harchaoui

State-of-the-art models are now trained with billions of parameters, reaching hardware limits in terms of memory consumption. This has created a recent demand for memory-efficient optimizers. To this end, we investigate the limits and…

Machine Learning · Computer Science 2019-02-14 Xinyi Chen , Naman Agarwal , Elad Hazan , Cyril Zhang , Yi Zhang

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Machine Learning · Computer Science 2023-02-03 Yesom Park , Jaemoo Choi , Changyeon Yoon , Chang hoon Song , Myungjoo Kang

We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…

Computation · Statistics 2024-02-22 Tahir Ekin , Roi Naveiro , Alberto Torres-Barrán , David Ríos-Insua

Standard autoregressive language models perform only polynomial-time computation to compute the probability of the next symbol. While this is attractive, it means they cannot model distributions whose next-symbol probability is hard to…

Machine Learning · Computer Science 2021-06-01 Chu-Cheng Lin , Aaron Jaech , Xin Li , Matthew R. Gormley , Jason Eisner

Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. In this paper we study how the…

Machine Learning · Computer Science 2020-02-11 Marc Khoury

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…

Machine Learning · Computer Science 2020-11-06 Patrick Kidger , James Morrill , James Foster , Terry Lyons

Trustworthy artificial intelligence increasingly relies on probabilistic computation to achieve robustness, interpretability, security and privacy. In practical systems, such workloads interleave deterministic data access with repeated…

Machine Learning · Computer Science 2026-03-27 Xueji Zhao , Likai Pei , Jianbo Liu , Kai Ni , Ningyuan Cao

When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with…

Machine Learning · Computer Science 2025-02-25 Dimitris Bertsimas , Arthur Delarue , Jean Pauphilet

We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…

Analysis of PDEs · Mathematics 2013-07-08 Elena Bonetti , Pierluigi Colli , Mauro Fabrizio , Gianni Gilardi

We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…

Optimization and Control · Mathematics 2025-11-25 Katya Scheinberg , Miaolan Xie

This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…

Dynamical Systems · Mathematics 2012-10-02 William Ott , Lai-Sang Young , Mikko Stenlund

Automatic numerical algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. The computational cost is often determined \emph{adaptively} by the algorithm based…

Numerical Analysis · Mathematics 2015-01-16 Nicholas Clancy , Yuhan Ding , Caleb Hamilton , Fred J. Hickernell , Yizhi Zhang

This work presents the first finite-time analysis for the last-iterate convergence of average-reward $Q$-learning with an asynchronous implementation. A key feature of the algorithm we study is the use of adaptive stepsizes, which serve as…

Machine Learning · Computer Science 2026-04-07 Zaiwei Chen , Phalguni Nanda

Parameter identification for mechanistic Ordinary Differential Equation (ODE) models underpins prediction and control in several applications, yet remains a manual and labor-intensive process: datasets are noisy and partial, models can be…

Computational Engineering, Finance, and Science · Computer Science 2025-09-16 Saakaar Bhatnagar