Related papers: Physics-Driven ML-Based Modelling for Correcting I…

The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…

Machine learning (ML) methods have recently been used as forward solvers to predict the mechanical properties of composite materials. Here, we use a supervised-autoencoder (sAE) to perform inverse design of graphene kirigami, where…

To control a dynamical system it is essential to obtain an accurate estimate of the current system state based on uncertain sensor measurements and existing system knowledge. An optimization-based moving horizon estimation (MHE) approach…

Evaluation in scientific reconstruction is dominated by pointwise metrics - RMSE, MAE, per-event resolution - under the implicit assumption that lower error means better reconstruction. We show that this assumption fails structurally for…

Efficient real-time solvers for forward and inverse problems are essential in engineering and science applications. Machine learning surrogate models have emerged as promising alternatives to traditional methods, offering substantially…

Complex physical simulations often require trade-offs between model fidelity and computational feasibility. We introduce Adaptive Online Emulation (AOE), which dynamically learns neural network surrogates during simulation execution to…

Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…

The idea of using machine learning (ML) methods to reconstruct the dynamics of a system is the topic of recent studies in the geosciences, in which the key output is a surrogate model meant to emulate the dynamical model. In order to treat…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

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…

Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…

The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…

Execution-based evaluation of LLM-generated code implicitly treats successful execution as a proxy for correctness. In scientific simulation, this proxy is insufficient: a generated input file can run, mesh, and converge while encoding…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

Inverse problems are the task of calibrating models to match data. They play a pivotal role in diverse engineering applications by allowing practitioners to align models with reality. In many applications, engineers and scientists do not…

Estimating the generalization error (GE) of machine learning models is fundamental, with resampling methods being the most common approach. However, in non-standard settings, particularly those where observations are not independently and…

Traffic state estimation (TSE) becomes challenging when probe-vehicle penetration is low and observations are spatially sparse. Pure data-driven methods lack physical explanations and have poor generalization when observed data is sparse.…

We present a Bayesian machine learning architecture that combines a physically motivated parametrization and an analytic error model for the likelihood with a deep generative model providing a powerful data-driven prior for complex signals.…

Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs) is a fundamental yet computationally challenging problem arising in domains such as diagnosis, planning, and structured prediction. In many practical…