arXiv subjects

Sascha Ranftl

Publications and source records attributed to Sascha Ranftl.

10 recordsLinked to original sources

arXiv2026

Uncertainty quantification in mechanics: A unified Bayesian perspective

Uncertainty quantification (UQ) is essential to experimental mechanics, but has become particularly relevant in computational mechanics, manifesting in two fundamental problem types: forward and inverse problems. The former addresses how input uncertainties propagate to the quantities of interest, whereas the latter aims to infer unknown parameters from experimental observations or simulations. Since efficient propagation typically requires a prohibitive number of evaluations to compute marginal output distributions, the development of fast, data-driven surrogate models becomes necessary. Thus, we can distinguish between two inverse tasks: (i) the identification and calibration of input uncertainties, and (ii) the construction of surrogates, a methodology collectively referred to as surrogate-based UQ. Building on probabilistic reasoning and the concept of partial belief, we demonstrate that Bayesian probability theory provides a unified theoretical framework for addressing both problem types. We further show that Bayesian inference allows for the seamless incorporation of essential subproblems, including model selection for identifying the most probable model specifications and experimental design for optimizing data collection by identifying experiments or simulations that maximize expected information gain about parameters, among others such as connections to sensitivity analysis or the use of special priors like random fields. While this theoretical framework is presented for general mechanical problems, particular emphasis is placed on biomechanics, where variability and uncertainty is especially pronounced due to inherent biological heterogeneity, patient-specific variability, and noisy data.

physics.comp-ph↗

arXiv2026

Regime-Adaptive Bayesian Optimization via Dirichlet Process Mixtures of Gaussian Processes

Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with locally-optimized hyperparameters. We derive collapsed Gibbs sampling that analytically marginalizes latent functions for efficient inference, and introduce adaptive concentration parameter scheduling for coarse-to-fine regime discovery. Our acquisition functions decompose uncertainty into intra-regime and inter-regime components. Experiments on synthetic benchmarks and real-world applications, including molecular conformer optimization, virtual screening for drug discovery, and fusion reactor design, demonstrate consistent improvements over state-of-the-art baselines on multi-regime objectives.

cs.LG↗

arXiv2025

Deep Polynomial Chaos Expansion

Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to the distribution of uncertain input parameters - PCE enables tractable inference of key statistical quantities such as (conditional) means, variances, covariances, and Sobol sensitivity indices, which are essential for understanding the modeled system and identifying influential parameters and their interactions. The applicability of PCE to high-dimensional problems is limited by poor scalability, as the number of basis functions grows exponentially with the number of parameters. In this paper, we address this challenge by combining PCE with ideas from tractable probabilistic circuits, resulting in deep polynomial chaos expansion (DeepPCE) - a deep generalization of PCE that scales effectively to high-dimensional input spaces. DeepPCE achieves predictive performance comparable to that of multilayer perceptrons (MLPs), while retaining PCE's ability to compute exact statistical inferences via simple forward passes. In contrast, such computations in MLPs require costly and often inaccurate approximations, such as Monte Carlo integration.

cs.LG↗

arXiv2024

Geometric Uncertainty of Patient-Specific Blood Vessels and its Impact on Aortic Hemodynamics

In the context of numerical simulations of the vascular system, local geometric uncertainties have not yet been examined in sufficient detail due to model complexity and the associated large numerical effort. Such uncertainties are related to geometric modeling errors resulting from computed tomography imaging, segmentation and meshing. This work presents a methodology to systematically induce local modifications and perform a sufficient number of blood flow simulations to draw statistically relevant conclusions on the most commonly employed quantities of interest, such as flow rates or wall shear stress. The surface of a structured hexahedral mesh of a patient-specific aorta is perturbed by displacement maps defined via Gaussian random fields to stochastically model the local uncertainty of the boundary. Three different cases are studied, with the mean perturbation magnitude of $0.25$, $0.5$ and $1.0~$mm. Valid, locally perturbed meshes are constructed via an elasticity operator that extends surface perturbations into the interior. Otherwise, identical incompressible flow problems are solved on these meshes, taking physiological boundary conditions and Carreau fluid parameters into account. Roughly $300\,000$ three-dimensional non-stationary blood flow simulations are performed for the three different perturbation cases to estimate the probability distributions of the quantities of interest. Convergence studies justify the spatial resolution of the employed meshes. Overall, the results suggest that moderate geometric perturbations result in reasonable engineering accuracy (relative errors in single-digit percentage range) of the quantities of interest, with higher sensitivity for gradient-related measures, noting that the observed errors are not negligible.

physics.med-ph↗

arXiv2023

Robust Bayesian Target Value Optimization

We consider the problem of finding an input to a stochastic black box function such that the scalar output of the black box function is as close as possible to a target value in the sense of the expected squared error. While the optimization of stochastic black boxes is classic in (robust) Bayesian optimization, the current approaches based on Gaussian processes predominantly focus either on i) maximization/minimization rather than target value optimization or ii) on the expectation, but not the variance of the output, ignoring output variations due to stochasticity in uncontrollable environmental variables. In this work, we fill this gap and derive acquisition functions for common criteria such as the expected improvement, the probability of improvement, and the lower confidence bound, assuming that aleatoric effects are Gaussian with known variance. Our experiments illustrate that this setting is compatible with certain extensions of Gaussian processes, and show that the thus derived acquisition functions can outperform classical Bayesian optimization even if the latter assumptions are violated. An industrial use case in billet forging is presented.

cs.LG↗

arXiv2022

A connection between probability, physics and neural networks

We illustrate an approach that can be exploited for constructing neural networks which a priori obey physical laws. We start with a simple single-layer neural network (NN) but refrain from choosing the activation functions yet. Under certain conditions and in the infinite-width limit, we may apply the central limit theorem, upon which the NN output becomes Gaussian. We may then investigate and manipulate the limit network by falling back on Gaussian process (GP) theory. It is observed that linear operators acting upon a GP again yield a GP. This also holds true for differential operators defining differential equations and describing physical laws. If we demand the GP, or equivalently the limit network, to obey the physical law, then this yields an equation for the covariance function or kernel of the GP, whose solution equivalently constrains the model to obey the physical law. The central limit theorem then suggests that NNs can be constructed to obey a physical law by choosing the activation functions such that they match a particular kernel in the infinite-width limit. The activation functions constructed in this way guarantee the NN to a priori obey the physics, up to the approximation error of non-infinite network width. Simple examples of the homogeneous 1D-Helmholtz equation are discussed and compared to naive kernels and activations.

stat.ML↗

arXiv2022

Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate

Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape, and type, are difficult to predict. Motivated by this observation, we describe the heterogeneous distribution of elastic fiber degradation in the dissected aortic wall using a stochastic constitutive model. For this purpose, random field realizations, which model the stochastic distribution of degraded elastic fibers, are generated over a non-equidistant grid. The random field then serves as input for a uni-axial extension test of the pathological aortic wall, solved with the finite-element (FE) method. To include the microstructure of the dissected aortic wall, a constitutive model developed in a previous study is applied, which also includes an approach to model the degradation of inter-lamellar elastic fibers. Then to assess the uncertainty in the output stress distribution due to this stochastic constitutive model, a convolutional neural network, specifically a Bayesian encoder-decoder, was used as a surrogate model that maps the random input fields to the output stress distribution obtained from the FE analysis. The results show that the neural network is able to predict the stress distribution of the FE analysis while significantly reducing the computational time. In addition, it provides the probability for exceeding critical stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.

stat.ML↗

arXiv2021

Bayesian Surrogate Analysis and Uncertainty Propagation

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that are learned from a small set of simulation samples. The surrogate models are commonly chosen and deemed trustworthy based on heuristic measures, and substituted for the simulation in order to approximately propagate the simulation input uncertainties to the simulation output. In the process, the contribution of the uncertainties of the surrogate itself to the simulation output uncertainties are usually neglected. In this work, we specifically address the case of doubtful surrogate trustworthiness, i.e. non-negligible surrogate uncertainties. We find that Bayesian probability theory yields a natural measure of surrogate trustworthiness, and that surrogate uncertainties can easily be included in simulation output uncertainties. For a Gaussian likelihood for the simulation data, with unknown surrogate variance and given a generalized linear surrogate model, the resulting formulas reduce to simple matrix multiplications. The framework contains Polynomial Chaos Expansions as a special case, and is easily extended to Gaussian Process Regression. Additionally, we show a simple way to implicitly include spatio-temporal correlations. Lastly, we demonstrate a numerical example where surrogate uncertainties are in part negligible and in part non-negligible.

stat.ME↗

arXiv2019

Bayesian Analysis of Femtosecond Pump-Probe Photoelectron-Photoion Coincidence Spectra with Fluctuating Laser Intensities

This paper employs Bayesian probability theory for analyzing data generated in femtosecond pump-probe photoelectron-photoion coincidence (PEPICO) experiments. These experiments allow investigating ultrafast dynamical processes in photoexcited molecules. Bayesian probability theory is consistently applied to data analysis problems occurring in these types of experiments such as background subtraction and false coincidences. We previously demonstrated that the Bayesian formalism has many advantages, amongst which are compensation of false coincidences, no overestimation of pump-only contributions, significantly increased signal-to-noise ratio, and applicability to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, our approach allows running experiments at higher ionization rates, resulting in an appreciable reduction of data acquisition times. In addition to our previous paper, we include fluctuating laser intensities, of which the straightforward implementation highlights yet another advantage of the Bayesian formalism. Our method is thoroughly scrutinized by challenging mock data, where we find a minor impact of laser fluctuations on false coincidences, yet a noteworthy influence on background subtraction. We apply our algorithm to data obtained in experiments and discuss the impact of laser fluctuations on the data analysis.

physics.atom-ph↗

arXiv2018

Femtosecond photoexcitation dynamics inside a quantum solvent

The observation of chemical reactions on the time scale of the motion of electrons and nuclei has been made possible by lasers with ever shortened pulse lengths. Superfluid helium represents a special solvent that permits the synthesis of novel classes of molecules that have eluded dynamical studies so far. However, photoexcitation inside this quantum solvent triggers a pronounced response of the solvation shell, which is not well understood. Here we present a mechanistic description of the solvent response to photoexcitation of indium (In) dopant atoms inside helium nanodroplets (He$_\mathrm{N}$), obtained from femtosecond pump-probe spectroscopy and time-dependent density functional theory simulations. For the In-He$_\mathrm{N}$ system, part of the excited state electronic energy leads to expansion of the solvation shell within 600 fs, initiating a collective shell oscillation with a period of about 30 ps. These coupled electronic and nuclear dynamics will be superimposed on intrinsic photoinduced processes of molecular systems inside helium droplets.

physics.atm-clus↗