arXiv subjects

P. S. Koutsourelakis

Publications and source records attributed to P. S. Koutsourelakis.

9 recordsLinked to original sources

arXiv2026

The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problems

Inferring the mechanical properties of soft tissues from measured deformations is a fundamental challenge in elastography. A rarely examined assumption underlying existing approaches is that the assumed constitutive law correctly describes the imaged material. When it fails, inversion still yields plausible-looking estimates - an illusion of fit with no indication of local model invalidity, which can mislead clinical interpretation. We propose a probabilistic framework that transforms constitutive model validity from an implicit assumption into an explicit, spatially resolved inference target. The key is to treat the stress field as an independent latent variable rather than deriving it from the constitutive law. This enables a pointwise comparison between the stress required by mechanical equilibrium and the stress predicted by the assumed constitutive model. Both governing equations enter the probabilistic learning objective as virtual observables with separate precision hyperparameters: the conservation law precision is set a priori to a small value reflecting its undisputed validity, while the constitutive precision is inferred under a sparsity-promoting prior. The resulting constitutive precision field provides an uncertainty-aware map of where the assumed model is supported by the data and where it is not. Inference is carried out via stochastic variational inference and is forward-model-free. We validate the framework on synthetic harmonic elastography experiments on a brain-slice geometry with an anisotropic inclusion. The inferred precision field identifies the inclusion with a five-order-of-magnitude precision contrast against the valid domain, robustly across 25-35 dB noise and four-fold sparser observations. A phantom experiment with ultrasound measurements on a linear elastic material yields no false-positive violations and recovers the true stiffness contrast.

stat.ML↗

arXiv2025

Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Data

Coarse-grained (CG) models provide an effective route to reducing the complexity of molecular simulations (MD), but conventional approaches depend heavily on long all-atom MD trajectories to adequately sample configurational space. This data dependence limits accuracy and generalizability, as unvisited configurations remain excluded from the resulting CG models. We introduce a fully data-free, generative framework for CG that directly targets the all-atom Boltzmann distribution. The model defines a structured latent space comprising slow collective variables, associated with multimodal marginal densities capturing metastable states, and fast variables, represented through simple, unimodal conditional distributions. A learnable, bijective map from latent space to atomistic coordinates enables the automatic and accurate reconstruction of molecular structures. Training relies solely on the interatomic potential and minimizes the reverse Kullback-Leibler (KL) divergence via an energy-based objective. To stabilize optimization and ensure mode coverage, we employ an adaptive tempering scheme that promotes the exploration of diverse configurations. Once trained, the model can generate independent, one-shot equilibrium samples at full atomic resolution. Validation on two synthetic systems, a double-well potential and a Gaussian mixture model, as well as on the benchmark alanine dipeptide, demonstrates that the method captures all relevant modes of the Boltzmann distribution, reconstructs atomic configurations, and automatically learns physically meaningful CG representations. These results suggest a promising, data-free alternative to traditional CG techniques, offering both a principled approach to addressing the long-standing "chicken-and-egg" challenge in coarse-graining and an effective solution to the back-mapping problem by enabling accurate reconstruction of all-atom configurations.

physics.chem-ph↗

arXiv2018

Physics-constrained, data-driven discovery of coarse-grained dynamics

The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven discovery for extract- ing governing equations by employing fine-scale simulation data. In particular, we cast the coarse-graining process under a probabilistic state-space model where the transition law dic- tates the evolution of the CG state variables and the emission law the coarse-to-fine map. The directed probabilistic graphical model implied, suggests that given values for the fine- grained (FG) variables, probabilistic inference tools must be employed to identify the cor- responding values for the CG states and to that end, we employ Stochastic Variational In- ference. We advocate a sparse Bayesian learning perspective which avoids overfitting and reveals the most salient features in the CG evolution law. The formulation adopted enables the quantification of a crucial, and often neglected, component in the CG process, i.e. the pre- dictive uncertainty due to information loss. Furthermore, it is capable of reconstructing the evolution of the full, fine-scale system. We demonstrate the efficacy of the proposed frame- work in high-dimensional systems of random walkers.

physics.comp-ph↗

arXiv2016

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un- known (latent) variables is high. This is the setting in many problems in com- putational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse prob- lems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, is a formidable task. The goal of the present paper is two- fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors, and on the other, to ex- tend our work in [1] with regards to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the model proposed by employing Importance Sam- pling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical di- agnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

stat.CO↗

arXiv2015

A novel Bayesian strategy for the identification of spatially-varying material properties and model validation: an application to static elastography

The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial variability that account for the various sources of uncertainty. On the other hand we attempt to address the question of model fidelity in relation to the experimental reality and particularly in the context of the material constitutive law adopted. This is especially important in biomedical settings when the inferred material properties will be used to make decisions/diagnoses. We propose an expanded parametrization that enables the quantification of model discrepancies in addition to the constitutive parameters. We propose scalable computational strategies for carrying out inference and learning tasks and demonstrate their effectiveness in numerical examples with noiseless and noisy synthetic data.

stat.CO↗

arXiv2015

Sparse Variational Bayesian Approximations for Nonlinear Inverse Problems: applications in nonlinear elastography

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem over an appropriately selected family of distributions. The goal is two-fold. Firstly, to find lower-dimensional representations of the unknown parameter vector that capture as much as possible of the associated posterior density, and secondly to enable the computation of the approximate posterior density with as few forward calls as possible. We discuss how these objectives can be achieved by using a fully Bayesian argumentation and employing the marginal likelihood or evidence as the ultimate model validation metric for any proposed dimensionality reduction. We demonstrate the performance of the proposed methodology for problems in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. An Importance Sampling scheme is finally employed in order to validate the results and assess the efficacy of the approximations provided.

stat.AP↗

arXiv2010

Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations

The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same objective. It offers rigorous convergence diagnostics even though history dependent, non-Markovian dynamics are employed. It makes use of a greedy optimization scheme in order to obtain sparse representations of the free energy function which can be particularly useful in multidimensional cases. It employs embarrassingly parallelizable sampling schemes that are based on adaptive Sequential Monte Carlo and can be readily coupled with legacy molecular dynamics simulators. The sequential nature of the learning and sampling scheme enables the efficient calculation of free energy functions parametrized by the temperature. The characteristics and capabilities of the proposed method are demonstrated in three numerical examples.

math-ph↗

arXiv2010

Scalable Bayesian reduced-order models for high-dimensional multiscale dynamical systems

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical interest is computationally infeasible or impractical. In complex systems, with limited physical insight on the coherent behavior of their constituents, the only available information is data obtained from simulations of the trajectories of huge numbers of degrees of freedom over microscopic time scales. This paper discusses a Bayesian approach to deriving probabilistic coarse-grained models that simultaneously address the problems of identifying appropriate reduced coordinates and the effective dynamics in this lower-dimensional representation. At the core of the models proposed lie simple, low-dimensional dynamical systems which serve as the building blocks of the global model. These approximate the latent, generating sources and parameterize the reduced-order dynamics. We discuss parallelizable, online inference and learning algorithms that employ Sequential Monte Carlo samplers and scale linearly with the dimensionality of the observed dynamics. We propose a Bayesian adaptive time-integration scheme that utilizes probabilistic predictive estimates and enables rigorous concurrent s imulation over macroscopic time scales. The data-driven perspective advocated assimilates computational and experimental data and thus can materialize data-model fusion. It can deal with applications that lack a mathematical description and where only observational data is available. Furthermore, it makes non-intrusive use of existing computational models.

stat.ML↗

arXiv2008

A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in PDE-based models and correspond to quantities such as density or pressure fields, elasto-plastic moduli and internal variables in solid mechanics, conductivity fields in heat diffusion problems, permeability fields in fluid flow through porous media etc. The proposed model has all the advantages of traditional Bayesian formulations such as the ability to produce measures of confidence for the inferences made and providing not only predictive estimates but also quantitative measures of the predictive uncertainty. In contrast to existing approaches it utilizes a parsimonious, non-parametric formulation that favors sparse representations and whose complexity can be determined from the data. The proposed framework in non-intrusive and makes use of a sequence of forward solvers operating at various resolutions. As a result, inexpensive, coarse solvers are used to identify the most salient features of the unknown field(s) which are subsequently enriched by invoking solvers operating at finer resolutions. This leads to significant computational savings particularly in problems involving computationally demanding forward models but also improvements in accuracy. It is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling which is embarrassingly parallelizable and circumvents issues with slow mixing encountered in Markov Chain Monte Carlo schemes.

math-ph↗