Related papers: Data preprocessing for parameter estimation. An ap…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…

Diffusion models have emerged as powerful generative priors for high-dimensional inverse problems, yet learning them when only corrupted or noisy observations are available remains challenging. In this work, we propose a new method for…

Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…

Numerical modeling of proton exchange membrane fuel cells is at the verge of becoming predictive. A crucial requisite for this, though, is that material properties of the membrane-electrode assembly and their functional dependence on the…

Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…

We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…

A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…

Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…

We discuss a theoretical model for bidirectional cargo transport in biological cells, which is driven by teams of molecular motors and subject to thermal fluctuations. The model describes explicitly the directed motion of the molecular…

This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…

Diffusion models have found phenomenal success as expressive priors for solving inverse problems, but their extension beyond natural images to more structured scientific domains remains limited. Motivated by applications in materials…

There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…

Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…