22 papers · ranked by Valyu relevance
A. Gallet, S. Rigby, T. N. Tallman, X. Kong + 6 more
'A. Liew' 'D. Liu' 'L. Chen' 'A. Hauptmann' 'D. Smyl'] The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural responses given data…
Ali Mohammad-Djafari, Wolfgang von der Linden, Sascha Ranftl
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed.…
Shima Kamyab, Zohreh Azimifar, Rasool Sabzi, Paul Fieguth + 1 more
In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep Regularizer. We choose a sample of each inverse problem type, so as to compare…
Danny Smyl, Andreas Hauptmann, Tyler Tallman
1. ## Introduction Inverse problems have always been about peering through a mirror-looking backwards from the things we can measure to learn about the things we cannot directly see. In the last few years, that mirror has been polished by faster algorithms, smarter statistics and a new ally in machine learning. In the…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Nan Ye, Farbod Roosta-Khorasani, Tiangang Cui
Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging…
Anonymous Anonymous
A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve these PDE…
Guillermo Rus, Juan Melchor
Optimizing an experimental design is a complex task when a model is required for indirect reconstruction of physical parameters from the sensor readings. In this work, a formulation is proposed to unify the probabilistic reconstruction of mechanical parameters and an optimization problem. An information-theoretic…
Sumit Tewari, Sahar Yousefi, Andrew Webb
We present a combination of a CNN-based encoder with an analytical forward map for solving inverse problems. We call it an encoder-analytic (EA) hybrid model. It does not require a dedicated training dataset and can train itself from the connected forward map in a direct learning fashion. A separate regularization term…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Ourania Giannopoulou
Magnetoencephalography (MEG) forward and inverse modeling is fundamental to neuroscientific discovery, yet the inversion of partial differential equations (PDEs) remains one of the most difficult challenges due to its inherent ill-posedness. While traditional numerical methods often struggle with the computational…
A. S. Leonov, Anatoly B. Bakushinsky
An inverse problem of acoustic sounding is under consideration in a form of 3D inverse coefficient problem for wave equation. Unknown coefficient is the local propagation velocity of vibrations, which is associated with inhomogeneities of the medium. We are looking for this coefficient, knowing special time integrals…
Ágota Figula
In this paper we consider the following Cauchy problem for second order hyperbolic differential equations: find a solution u(x, y) of the equation by the initial conditions u|y=0 = τ (x), uy|y=0 = ν(x), where ν(x) ∈ C 1 (R), τ (x) ∈ C 2 (R) are given functions such that ν(x) is once-, and τ (x) is twice-continuously…
Yue Mei, Jiahao Liu, Xu Guo, Brandon Zimmerman + 2 more
This paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving…
Mansur I. Ismailov, Sait Erkovan
We consider an inverse problem of determining the time-dependent lowest order coefficient of two-dimensional (2D) heat equation with Ionkin boundary and total energy integral overdetermination condition. The well-posedness of the problem is obtained by generalized Fourier method combined by the Banach fixed poind…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We…
Krzysztof Rykaczewski, Jan Nikadon, Włodzisław Duch, Tomasz Piotrowski
Recognition and interpretation of brain activity patterns from EEG or MEG signals is one of the most important tasks in cognitive neuroscience, requiring sophisticated methods of signal processing. The supFunSim library is a new Matlab toolbox which generates accurate EEG forward models and implements a collection of…
Tianfan Jin, Brett M Savoie
Contemporary machine learning algorithms have largely succeeded in automating the development of mathematical models from data. Although this is a striking accomplishment, it leaves unaddressed the multitude of scenarios, especially across the chemical sciences and engineering, where deductive, rather than inductive…
Charles Eads
This report describes and illustrates a set of automatable multicomponent exponential relaxation analysis protocols that are model-agnostic and suited to extracting information under circumstances when little prior knowledge about the underlying system is used. Methods are illustrated and mathematical and physical…
David R. Stoutemyer
A strict integer Laurent polynomial in a variable x is 0 or a sum of one or more terms having integer coefficients times x raised to a negative integer exponent. Equations that can be transformed to certain such polynomials times exp(−x) = constant are exactly solvable by inverses of modified spherical Bessel functions…
Rumiana Tenchov, Qiongqiong Angela Zhou
Inverse vaccines are a new and exciting approach to treating autoimmune diseases. Unlike traditional vaccines that train the immune system to fight off pathogens, inverse vaccines aim to reprogram the immune system to stop attacking healthy tissues.
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…