Related papers: Solving Inverse Problems in Stochastic Self-Organi…

Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…

Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different…

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…

Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…

A broad class of problems at the core of computational imaging, sensing, and low-level computer vision reduces to the inverse problem of extracting latent images that follow a prior distribution, from measurements taken under a known…

Given a set of human's decisions that are observed, inverse optimization has been developed and utilized to infer the underlying decision making problem. The majority of existing studies assumes that the decision making problem is with a…

Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…

This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…

Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

We introduce inverse transport networks as a learning architecture for inverse rendering problems where, given input image measurements, we seek to infer physical scene parameters such as shape, material, and illumination. During training,…

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Natural language processing has made significant inroads into learning the semantics of words through distributional approaches, however representations learnt via these methods fail to capture certain kinds of information implicit in the…

In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…

Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…

We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…

In many complex dynamical systems, artificial or natural, one can observe self-organization of patterns emerging from local rules. Cellular automata, like the Game of Life (GOL), have been widely used as abstract models enabling the study…

State-of-the-art methods in generative representation learning yield semantic disentanglement, but typically do not consider physical scene parameters, such as geometry, albedo, lighting, or camera. We posit that inverse rendering, a way to…