@article{AndresArconesWeiserKoutsourelakisetal.2026, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Phaedon-Stelios and Unger, J{\"o}rg F.}, title = {Embedded Model Form Uncertainty Quantification with Measurement Noise for Bayesian Model Calibration}, volume = {7}, journal = {Data-Centric Engineering}, arxiv = {http://arxiv.org/abs/2410.12037}, doi = {10.1017/dce.2025.10035}, year = {2026}, abstract = {A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. Nevertheless, Bayesian methods paired with inexact models usually produce predictions unable to represent the observed datapoints. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs. This paper introduces a more interpretable framework for embedding the model inadequacy compared to existing methods. To overcome the limitations of current approaches, we adapt the existing likelihood models to properly account for noise in the measurements and propose two new formulations designed to address their shortcomings. Moreover, we evaluate the performance of this inadequacy-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the model inadequacy term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction's reliability. Finally, the proposed approach is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation using temperature bservations.}, language = {en} } @article{LelievreZhang2019, author = {Leli{\`e}vre, Tony and Zhang, Wei}, title = {Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates}, journal = {Multiscale Modeling and Simulation}, number = {17}, arxiv = {http://arxiv.org/abs/1805.01928}, doi = {10.1137/18M1186034}, pages = {1019 -- 1051}, year = {2019}, abstract = {Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli{\`e}vre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Leli{\`e}vre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued.}, language = {en} } @article{HartmannSchuetteZhang2019, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms}, volume = {175}, journal = {Journal of Statistical Physics}, number = {6}, arxiv = {http://arxiv.org/abs/1803.09347}, doi = {10.1007/s10955-019-02286-4}, pages = {1214 -- 1261}, year = {2019}, abstract = {In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.}, language = {en} } @article{Zhang2021, author = {Zhang, Wei}, title = {Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes}, volume = {62}, journal = {Journal of Mathematical Physics}, number = {4}, arxiv = {http://arxiv.org/abs/2006.11212}, doi = {10.1063/5.0038740}, pages = {26}, year = {2021}, abstract = {This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to the transient invariant probability measures. We also study the time reversal of the reverse process in Crooks' fluctuation theorem. We show that the time reversal of the reverse process coincides with the optimally controlled forward process that leads to zero variance importance sampling estimator based on Jarzynski's equality.}, language = {en} } @article{LelievreStoltzZhang2022, author = {Lelievre, Tony and Stoltz, Gabriel and Zhang, Wei}, title = {Multiple projection MCMC algorithms on submanifolds}, journal = {IMA Journal of Numerical Analysis}, arxiv = {http://arxiv.org/abs/2003.09402}, doi = {10.1093/imanum/drac006}, year = {2022}, abstract = {We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples.}, language = {en} } @article{ZhangLiSchuette2022, author = {Zhang, Wei and Li, Tiejun and Sch{\"u}tte, Christof}, title = {Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks}, volume = {465}, journal = {Journal of Computational Physics}, arxiv = {http://arxiv.org/abs/2110.14523}, doi = {10.1016/j.jcp.2022.111377}, year = {2022}, abstract = {In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.}, language = {en} } @article{ZhangKlusConradetal.2019, author = {Zhang, Wei and Klus, Stefan and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Learning chemical reaction networks from trajectory data}, volume = {18}, journal = {SIAM Journal on Applied Dynamical Systems (SIADS)}, number = {4}, arxiv = {http://arxiv.org/abs/1902.04920}, doi = {10.1137/19M1265880}, pages = {2000 -- 2046}, year = {2019}, abstract = {We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.}, language = {en} } @article{ZhaoZhangLi2024, author = {Zhao, Yue and Zhang, Wei and Li, Tiejun}, title = {EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation}, volume = {11}, journal = {National Science Review}, number = {7}, doi = {10.1093/nsr/nwae052}, year = {2024}, abstract = {We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness, and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an 8D limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.}, language = {en} } @article{AkhyarZhangStoltzetal.2025, author = {Akhyar, Fatima-Zahrae and Zhang, Wei and Stoltz, Gabriel and Sch{\"u}tte, Christof}, title = {Generative modeling of conditional probability distributions on the level-sets of collective variables}, arxiv = {http://arxiv.org/abs/2512.17374}, year = {2025}, abstract = {Given a probability distribution \$\mu\$ in \$\mathbb{R}^d\$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable \$\xi: \mathbb{R}^d \rightarrow \mathbb{R}^k\$, where \$1 \le k t0. We obtain promising results assuming Newtonian cooling for boxes filled with air, heaps of clothes, or books in two different experimental scenarios. Two different parameter estimators, (TA0^, t0^) based on four temperature measurements and (TA0*, t0*) for 4N measurements were tested. Our results in a climate chamber were partially appropriate for TTDE input. A decline at time t0 from TA0 = 22.5°C ↓ TA1 = 14°C was reconstructed at t = t0 + 95min with relative deviations ρt0^ = 27\% and ρTA0^ = 19\% relative to t - t0 and TA0 - TA1 respectively, for N = 1 with span Δt = 50min. For N = 200 in a time interval [t0 + 95min, t0 + 295min] we found ρt0^ = 5\% and ρTA0^ = 11\% with the same Δt. Further research is necessary to guarantee applicability in routine casework, in particular with respect to more elaborate cooling models, estimation algorithms, and evaluation localization.}, language = {en} } @article{VillaniAndresArconesUngeretal.2026, author = {Villani, Paolo and Andr{\´e}s Arcones, Daniel and Unger, J{\"o}rg F. and Weiser, Martin}, title = {Gaussian mixture models for model improvement}, arxiv = {http://arxiv.org/abs/2603.15101}, year = {2026}, abstract = {Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even after model calibration due to the model discrepancy, which may result from deliberate modeling decisions, ignorance, or lack of knowledge. If the mismatch between simulation and measurements are deemed unacceptable, the model has to be improved. Targeted model improvement is challenging due to a non-local impact of model discrepancies on measurements and the dependence on sensor configurations. Many approaches to model improvement, such as Bayesian calibration with additive mismatch terms, gray-box models, symbolic regression, or stochastic model updating, often lack interpretability, generalizability, physical consistency, or practical applicability. This paper introduces a non-intrusive approach to model discrepancy analysis using mixture models. Instead of directly modifying the model structure, the method maps sensor readings to clusters of physically meaningful parameters, automatically assigning sensor readings to parameter vector clusters. This mapping can reveal systematic discrepancies and model biases, guiding targeted, physics-based refinements by the modeler. The approach is formulated within a Bayesian framework, enabling the identification of parameter clusters and their assignments via the Expectation-Maximization (EM) algorithm. The methodology is demonstrated through numerical experiments, including an illustrative example and a real-world case study of heat transfer in a concrete bridge.}, language = {en} } @misc{BaumannDudaSchielaetal.2026, author = {Baumann, Felix and Duda, Georg and Schiela, Anton and Weiser, Martin}, title = {Identification of Stress in Heterogeneous Contact Models}, volume = {173}, journal = {Non-Smooth and Complementarity-Based Distributed Parameter Systems}, editor = {Hinterm{\"u}ller, Michael and Herzog, Roland and Kanzow, Christian and Ulbrich, Michael and Ulbrich, Stefan}, publisher = {Springer Nature}, year = {2026}, abstract = {We develop a heterogeneous model of the lower limb system to simulate muscle forces and stresses acting on the knee joint. The modelling of the bone dynamics leads to an index-3 DAE, which we discretize by higher order collocation methods. Furthermore, we present an elastomechanical contact knee joint model of the articular cartilage. For the solution of the contact problem we develop an efficient multigrid solver, based on an Augmented-Lagrangian relaxation of the contact constraints. We formulate the identification of joint forces and resulting stresses with respect to different knee joint models as an inverse problem based on medical gait data.}, language = {en} } @article{LueckeWinkelmannKoltai2026, author = {L{\"u}cke, Marvin and Winkelmann, Stefanie and Koltai, Peter}, title = {Accurate mean-field equation for voter model dynamics on scale-free networks}, volume = {113}, journal = {Physical Review E}, arxiv = {http://arxiv.org/abs/2509.13485}, doi = {10.1103/vkpx-5cvt}, pages = {034311}, year = {2026}, abstract = {Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The resulting approximations perform well on dense and homogeneous networks but poorly on scale-free networks, which, however, are more realistic in many applications. In this paper, we introduce a modified version of the mean-field approximation for voter model dynamics on scale-free networks. The two main deviations from classical theory are that we use degree-weighted shares as coarse variables and that we introduce a correlation factor that can be interpreted as slowing down dynamics induced by interactions. We observe that the correlation factor is only a property of the network and not of the state or of parameters of the process. This approach achieves a significantly smaller approximation error than standard methods without increasing dimensionality.}, language = {en} } @article{WehlitzPavliotisSchuetteetal.2026, author = {Wehlitz, Nathalie and Pavliotis, Grigorios and Sch{\"u}tte, Christof and Winkelmann, Stefanie}, title = {Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics}, arxiv = {http://arxiv.org/abs/2601.02932}, year = {2026}, abstract = {We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics.}, language = {en} }