26 papers · ranked by Valyu relevance
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…
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…
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…
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.…
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…
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…
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…
Alejandro Mata Ali
In this paper, we present a new formalism, the Field Tensor Network Integral Logical Operator (FTNILO), to obtain the explicit equation that returns the minimum, maximum, and zeros of a multivariable injective function, and an algorithm for non-injective ones. This method extends the MeLoCoToN algorithm for inversion…
Nasser Al-Salti, Mokhtar Kirane, Berikbol T. Torebek
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence and uniqueness of solutions to these problems are presented. Solutions are…
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…
Eva Abramov
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part of the quadratic form) provided that approximate estimates of the optimal…
Egor E. Chitorkin, Natalia P. Bondarenko
In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of recovering the potential and the polynomials from the Weyl function is proved. An…
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…
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…
Martin Robinson, Alan Bond, Alexandr Simonov, Jie Zhang + 1 more
Recently, we have introduced the use of techniques drawn from Bayesian statistics to recover kinetic and thermodynamic parameters from voltammetric data, and were able to show that the technique of large amplitude ac voltammetry yielded significantly more accurate parameter values than the equivalent dc approach. In…
Srinivas Kashyap Chilakamarri, Sneha Reddy Kasturi, Sai Pranav Reddy Yerrabandla, Sanjana Gogte + 1 more
Designing functional peptides with specific structural and biochemical properties is critical for applications in protein engineering and therapeutic discovery. However, most peptide design approaches rely on evolutionary or local sequence optimization methods, which are limited when adapting to peptides’ shorter…
Natalia P. Bondarenko, Vjacheslav Yurko
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove uniqueness of solution, global solvability, local solvability, and stability. Our…
Avi Barliya, Nili Krausz, Hila Naaman, Enrico Chiovetto + 2 more
The inverse kinematics problem deals with the question of how the nervous system coordinates movement to resolve redundancy, such as in the case of arm reaching movements where more degrees of freedom are available at the joint versus hand level. In particular, this work focuses on determining which coordinate frames…
Elina Shishkina
Keywords: Bessel operator, weighted spherical mean, mixed hyperbolic Riesz B–potential Abstract. The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new…
Patrick Dumond, Natalie Baddour
An inverse eigenvalue problem approach to system design is considered. The Cayley-Hamilton theorem is developed for the general case involving the generalized eigenvalue vibration problem. Since many solutions exist for a desired frequency spectrum, a discussion of the required design information and suggestions for…
Rafał Brociek, Agata Chmielowska, Damian Słota
This paper presents the algorithms for solving the inverse problems on models with the fractional derivative. The presented algorithm is based on the Real Ant Colony Optimization algorithm. In this paper, the examples of the algorithm application for the inverse heat conduction problem on the model with the fractional…
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…
Lukas Hecker
Electroencephalography (EEG) source imaging remains difficult to compare systematically because inverse solvers are distributed across different software packages, programming languages, and evaluation protocols. We present a frozen four-scenario EEG benchmark of 106 solvers evaluated on a shared BioSemi-32 / ico3…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a reaction mechanism of zymogen activation. The reaction consists of a primary non-observable zymogen activation reaction that it is coupled to an indicator (observable) reaction. The product of the first…
Authors not listed
Electrochemical measurements in concentrated electrolytes are intrinsically sensitive to non-ideal chemical potentials, yet they are commonly interpreted using assumed activity models rather than exploited as thermodynamic constraints. In this work, we introduce an inverse electrochemical framework in which macroscopic…
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.