Deep data consistency: A fast and robust diffusion model-based solver for inverse problems.

This data article presents an experimental dataset of scattered images, obtained using a low-cost, open-source, Raspberry Pi-based optical system. Each data sample includes two grayscale images of 256 × 256 resolution: the (i) scattered image, and (ii) original projected pattern as ground truth. The system projects diverse patterns using various optical diffusers with different scattering coefficients and physical thicknesses. The dataset includes geometric shapes, digits, and textures to increase variability and generalization. This variety allows the analysis of distinct scattering regimes and evaluation of image recovery models under varying optical complexities. The dataset supports deep learning research focused on inverse problems in optics. It is particularly useful for training and benchmarking image restoration models in scattering environments.

Convergence analysis of a PINNs-based approach to the inverse source problem of the heat equation with local measurements

Solving the inverse source problems for wave equation with final time measurements by a data driven approach

A physics-informed machine learning framework for inverse multi-solution problems

Increasing stability for inverse acoustic source problems in the time domain

A time-dependent inverse source problem for a semilinear pseudo-parabolic equation with Neumann boundary condition

Enhanced diagnosis of skin lesions through torsional wave propagation and probabilistic inverse problem algorithms: An experimental study

Solving the inverse problem of time-dependent heat source identification with non-classical boundary conditions

Physics-informed neural networks in water and wastewater systems: a critical review.

Inverse problems solutions using physics-informed neural networks with novel adaptive activation function

A stable iterative direct sampling method for elliptic inverse problems with partial Cauchy data

ABSTRACT The main difficulty in modeling turbulence/soot production interaction (TSI) in non-premixed flames stems from the strong correlation between soot quantities and mixture fraction in the soot oxidation region. This is due to the fast nature of the oxidation process, which limits the coexistence of soot and oxidative species in mixture fraction space. Consequently, the “uncorrelated” model, which neglects this correlation, overestimates soot oxidation rates by more than an order of magnitude. In the RANS context, a presumed-probability density function (PDF) model is proposed. This model combines the flamelet approach to express the gas-phase part of soot production rates as a function of a reduced set of parameters, with the conditional source-term estimation (CSE) model to obtain the conditional mean of soot mass fraction in mixture fraction space. This model is more general than existing presumed PDF models in the literature because the conditional means of soot mass fraction are retrieved from the CSE inverse problem without presuming their shape. It is, therefore, applicable to situations with both infinitely fast and finite-rate soot oxidation. The model relies on several hypotheses: 1) The first-order conditional moment closure (CMC) hypothesis; 2) A presumed-PDF for the flamelet parameters; 3) The conditional mean of the number density of soot primary particles is set equal to its mean value; 4) The conditional mean of soot mass fraction is decomposed into Bernstein basis polynomials and 5) A strategy based on temporal samples at a fixed location is proposed to build the CSE ensembles used to retrieve the Bernstein coefficients from the CSE inverse problem. This alternative definition of the CSE ensemble substitutes the classical one based on the radial homogeneity assumption, as soot does not strictly satisfy this assumption. These assumptions, along with the accuracy of the corresponding predicted mean soot oxidation by OH and soot surface growth rates, are assessed in the case of the Sandia ethylene non-premixed turbulent jet flame by comparison with reference solutions obtained from RANS/TPDF simulations. The hybrid flamelet/CSE-based model predicts reasonably well the mean soot oxidation and surface growth rates within about 30% and 20% of the TPDF solutions, respectively. It significantly improves the prediction of the “uncorrelated” model and outperforms flamelet-based presumed PDF models from the literature, while being more flexible. The model can be readily extended to large eddy simulation.

The advancement of intelligent surgery has imposed greater requirements on the precision and real-time performance of pulmonary minimally invasive surgical navigation. However, existing intraoperative navigation techniques, including optical tracking, X-ray imaging, and magnetic resonance imaging (MRI), have inherent limitations such as inadequate real-time performance, complicated workflows, strong equipment dependency, and restricted visual fields. These constraints hinder the ability of interventional surgeries to provide continuous and stable three-dimensional coordinate feedback in deep, non-line-of-sight environments. Therefore, this study proposes an electric current field source reconstruction method for determining the terminal coordinates of surgical actuators. An electric current is injected from the tip of the surgical instrument, creating an electric field within the human tissue. The potential measured by surface electrodes are then used to reconstruct the current source coordinates, enabling real-time and active sensing of the surgical probe coordinates. A mathematical model for electric current field-based coordinate positioning was developed, involving analyses of the forward and inverse problems as well as coordinate reconstruction. Random single-point positioning simulations were conducted, and a 16 + 1-electrodes experimental platform was constructed for coordinates navigation tests to evaluate positioning and navigation performance. In addition, dynamic positioning experiments of multiple physiological tissues were carried out to assess the robustness and anti-interference capability of the proposed method. Experimental results indicate that the positioning error remains within 2 mm under single-point, linear, and curved trajectory conditions, satisfying the precision requirements for intraoperative navigation. This method significantly improves the accuracy and safety of surgical positioning and navigation, thereby holding substantial engineering significance and clinical value for the advancement of intelligent surgical systems.

RNA design aims at constructing RiboNucleic Acids (RNA) sequences that perform a predefined biological function, usually modeled by multiple constraints on the sequence and structure level. In its most popular setting, called the inverse folding problem, designed RNAs should adopt a predefined target secondary structure, preferentially to any alternative structure. It was previously observed that some secondary structures are undesignable, i.e. no RNA sequence can fold uniquely into the target structure while satisfying some criterion measuring how preferential this folding is compared to alternative conformations. We show that the proportion of designable secondary structures decreases exponentially with the size of the target secondary structure, for various popular combinations of energy models and design objectives. This exponential decay is, at least in part, due to the existence of undesignable motifs, which can be generically constructed, and jointly analyzed to yield asymptotic upper-bounds on the number of designable structures. Finally, we define a lower bound of the minimal ensemble defect of a secondary structure. We show that, across uniformly distributed secondary structures, such lower bound admits a normal limiting distribution whose two parameters, the expected value and the variance, both growing linearly with the size of secondary structure.

Abstract We consider a first-order transport equation where d\ge 2, Ω is a bounded domain and 0 < t < T . We prove a Carleman estimate for more general condition on the principal coefficients H(x) than in the existing works. The key is the construction of a piecewise smooth weight function in x according to a suitable decomposition of Ω. Our assumptions on H generalize the conditions in the existing articles, and require that a directed graph created by the corresponding stream field has no closed loops. Then, we apply our Carleman estimate to two inverse problems of determinination of an initial value and one of a spatial factor of a source term, so that we establish Lipschitz stability estimates for the inverse problems.

Abstract We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract Cauchy problem using the solution operator representation. As a complement, we also study similar problems by considering almost sectorial operators that depend on a time-variable.

The advancement of nanophotonic devices is significantly dependent on achieving high-precision inverse design capabilities, which are critical for identifying optimal structural configurations that enable enhanced and multifunctional performances. The process of inverse design confronts a one-to-many relationship due to the complex mapping between optical performance and structure. Though several approaches, including tandem networks, mixture density networks (MDN), and conditional generative adversarial networks, have shown promising outcomes, they still face accuracy limitations when confronted with structures with higher degrees of freedom. Here, we propose a sampling-enhanced MDN called a mixture probability sampling network (MPSN), that outputs mixture Gaussian distributions (MGDs) of structural parameters through an end-to-end framework. The results of multiple samples drawn from the MGDs are fed into a pre-trained network, and the sample that minimizes the error relative to the real data is selected for network training. We benchmark the high performance in nanophotonics through the structural color design, achieving a high precision of up to 99.9% and a mean absolute error of less than 0.002. This work paves the way for resolving intricate inverse design problems in nanophotonics.

Abstract In this paper, we investigate an inverse source problem arising in bioluminescence tomography (BLT), where the objective is to recover both the support and intensity of the light source from boundary measurements. A shape optimization framework is developed, in which the source strength and its support are decoupled through first-order optimality conditions. To enhance the stability of the reconstruction, we incorporate a parameter-dependent coupled complex boundary method (CCBM) scheme together with perimeter and volume regularizations. The level-set representation naturally accommodates topological changes, enabling the reconstruction of multiple, closely located, or nested sources. Theoretical justifications are provided, and a series of numerical experiments are conducted to validate the proposed method. The results demonstrate the robustness, accuracy, and noise-resistance of the algorithm, as well as its advantages over existing approaches.

Abstract We demonstrate that system-agnostic physics-informed neural networks can efficiently learn the dynamical solution of quantum master equations, as compared to problem-specific numerical solvers, with respect to accuracy, stability of training convergence, robustness towards bath parameters or initial conditions, and equivalent convergence times for the non-Markovian evolution of two-level quantum systems. We study cases of quantum dot systems driven by external electromagnetic fields and coupled to an acoustic phonon environment, and analyze two problem setups, the evolution of Bloch vectorized coupled differential equations obtained from a Lindblad master equation and the evolution of a non-Markovian master equation obtained from the Nakajima-Zwanzig formulation. We implement a fully connected physics-informed neural network architecture to solve the two problems. We also use the same methodology to solve the inverse problem of estimation of bath parameters in a supervised fashion, but with a very limited number of noisy samples.