Probabilistic and Robust Engineering Design

Latest papers

• S$^{2}$-PINN: Stochastic Separable Physics-Informed Neural Networks

  Zhendong Li, Akwum Onwunta · 5 October 2026

  Uncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for this class of problems face the curse of dimensionality, and existing neural solvers often ignore the stochastic structure …

• Tangent Schr\"odinger Bridge Matching: Learning Stochastic Transport with Mechanistic Sensitivities

  Jowaria Khan, Elizabeth Bondi-Kelly · 5 October 2026

  Predicting how stochastic systems respond to changes in viscosity, reaction rates, or external forces requires costly simulations, motivating reusable learned models. Yet matching observed outcome distributions does not ensure accurate intervention responses. We introduce Tangent Schr\"odinger Bridg…

• Threshold-Aware Conformal Routing

  Shiwei Tan, Huzefa Rangwala, Danielle C. Maddix · 5 October 2026

  High-fidelity simulations are essential to scientific and engineering design, but can be expensive to run repeatedly. Learned surrogates offer a faster alternative, yet their higher errors may alter downstream decisions. This accuracy-speed tradeoff creates a need to determine whether a surrogate ca…

• Uncertainty and Explainability in Deep Rough Volatility: A Neural Information-Theoretic Posterior Approach

  Damiano Brigo, Rapha\"el Huser, Dan Leonte · 28 September 2026

  Deep learning has substantially accelerated the calibration of complex stochastic-volatility models, but neural point calibration alone does not capture the uncertainty remaining after an implied-volatility (IV) surface has been observed. We develop a simulation-based inference framework for rough H…

• Predictive Uncertainty for Neural CAE Surrogates

  Kaustubh Tangsali, Mohammad Amin Nabian, Kelvin Lee, Carmelo Gonzales, Sanjay Choudhry · 23 September 2026

  Neural surrogates can substantially accelerate computer-aided engineering (CAE) workflows, but their use in design requires uncertainty estimates that remain meaningful across varying geometries, spatial prediction fields, and engineering quantities of interest. We investigate how established uncert…

• Rare Event Estimation via Iterative Unalignment

  Hanming Yang, Daksh Mittal, Jing Dong, Hongseok Namkoong · 22 September 2026

  As agents are deployed with increased autonomy, even extremely rare events along their stochastic output trajectories can occur and prove catastrophic. Safe deployment therefore does not depend on whether these events can occur, but on how often they might. We study the problem of estimating the pro…

• Multivariate quantile regression via Kolmogorov-Arnold Networks

  Andrew Polar, Michael Poluektov · 22 September 2026

  This paper introduces a novel algorithm for predicting conditional joint distributions of vector-valued targets in stochastic systems whose randomness is intrinsic rather than arising from observation errors or additive noise. Multivariate quantile regression also involves modeling conditional joint…

• Compressed Active Subspaces for Scalable Bayesian Inference

  Thomas Flynn, Sanket Jantre, Byung-Jun Yoon, Kibaek Kim · 18 September 2026

  Active subspace methods provide a framework for quantifying predictive uncertainty in high-dimensional models by identifying and performing inference along parameter directions that have the greatest influence on the model output. However, the construction of active subspaces requires storing many f…

• A Weighted Kernel Method for Approximation that Adapts to Learned Multivariable Structure

  John E. Darges, Laura Weidensager · 16 September 2026

  Approximating the input-output behavior of a multivariable black-box function from limited data is challenging when blind to the importance of its inputs and their interactions. We introduce total sensitivity kernels (TSKs), a method based on families of weighted ANOVA kernels that learn and adapt t…

• 3D Field Data Reduction with Adaptive Sample-Based Gaussian-Encoded Reconstruction

  Michael R. Martin, Joseph Insley, Victor A. Mateevitsi, Silvio Rizzi, Kwan-Liu Ma · 16 September 2026

  In scientific simulation, regular grids, unstructured meshes, and particle-based formats are chosen to represent field data for computational efficiency, geometry/adaptive flexibility, and following motion/deformation, respectively. Each of these field data formats is often handled through separate …

• Estimating Inconsistency Response Surfaces under Uncertainty in Cyber-Physical System Development

  Johannes M\"akelburg, Tim Schwabe, Maribel Acosta · 11 September 2026

  Cyber-Physical Systems (CPS) are commonly represented through multiple interconnected models. During development, CPS consistency requires that shared model elements remain compatible across these models. Uncertainty, for example, due to sensor noise or model abstraction, changes the admissible valu…

• Uncertainty Quantification in Machine Learning for Biosignal Applications -- A Review

  Ivo Pascal de Jong, Andreea Ioana Sburlea, Matias Valdenegro-Toro · 4 September 2026

  Purpose: Uncertainty Quantification (UQ) has gained traction in an attempt to improve the interpretability and robustness of machine learning predictions. Specifically (medical) biosignals such as electroencephalography (EEG), electrocardiography (ECG), electrooculography (EOG), and electromyography…

• Conformal Uncertainty Quantification Guarantees for Neural Operators

  Tom Stent, Nicolas Boull\'e · 31 August 2026

  Neural operators provide fast surrogate models for approximating operators between function spaces, but their predictions often lack uncertainty quantification. We develop a split conformal framework to guarantee that a calibrated pointwise band around the neural operator output contains the true so…

• It depends: Incorporating correlations for joint aleatoric and epistemic uncertainties of high-dimensional output spaces

  Leonhard F. Feiner, Manuel Nickel, Martin Menten, Laurin Lux, Rickmer Braren, Daniel Rueckert, Georgios Kaissis, Raphael Rehms, Johannes Paetzold · 26 August 2026

  Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-dimensional output spaces. This paper addresses the dual nature of uncertainty -- aleatoric and epistemic -- focusing on their joint integration in hi…

• Heteroscedastic Neural Surrogate Modeling for Robust and Rapid Bayesian Inference in Fusion Plasma Diagnostics

  Liyun Zhang, Naoya Mamada, Kentaro Sakai, Takeo Hoshi, Toru Aonishi · 21 August 2026

  Bayesian inference via Markov Chain Monte Carlo (MCMC) provides effective parameter estimation, but its real-time application in complex physical systems is hindered by heavy computational bottlenecks and extreme sensitivity to statistical noise. We address this by proposing a neural-network-based p…

• Process Optimization Under Uncertainty for Improving the Bond Quality of Polymer Filaments in Fused Filament Fabrication

  Berkcan Kapusuzoglu, Matthew Sato, Sankaran Mahadevan, Paul Witherell · 20 August 2026

  This paper develops a computational framework to optimize the process parameters such that the bond quality between extruded polymer filaments is maximized in fused filament fabrication (FFF). A transient heat transfer analysis providing an estimate of the temperature profile of the filaments is cou…

• A Critical Synthesis of Uncertainty Quantification and Foundation Models for Semantic Segmentation

  Steven Landgraf, Joceline Hinz, Markus Ulrich · 20 August 2026

  Foundation models are increasingly breaking what seemed to be impossible not long ago by enabling unprecedented accuracy and cross-domain generalization. Yet their lack of interpretability, tendency to be overconfident, and sensitivity to real-world domain shifts pose critical challenges for safety-…

• Adaptive surrogate modeling for high-dimensional spatio-temporal output

  Berkcan Kapusuzoglu, Shunsaku Matsumoto, Yoshitomo Miyagi, Daigo Watanabe, Sankaran Mahadevan · 19 August 2026

  This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed t…

• Information fusion and machine learning for sensitivity analysis using physics knowledge and experimental data

  Berkcan Kapusuzoglu, Sankaran Mahadevan · 19 August 2026

  When computational models (either physics-based or data-driven) are used for the sensitivity analysis of engineering systems, the sensitivity estimate is affected by the accuracy and uncertainty of the model. This paper considers global sensitivity analysis (GSA) for situations where both a physics-…

• Coded Hankel Polynomial Chaos: Spectral Identification of Dominant Polynomial-Chaos Modes

  Zhiliang Deng, Xiaomei Yang · 18 August 2026

  Identification of dominant polynomial-chaos modes is usually formulated as a sparse-regression problem on a sampled multivariate polynomial dictionary. We develop coded Hankel polynomial chaos (CH-PC), a complementary spectral formulation for dominant-mode identification. A finite generating transfo…

• Scalable extensions to given-data Sobol' index estimators

  Teresa Portone, Bert Debusschere, Samantha Yang, Emiliano Islas-Quinones, T. Patrick Xiao · 11 August 2026

  Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing methods still preclude their application to models with an extreme…

• Tracing sources of epistemic uncertainty in deep learning predictions: homo- and hetero-scedastic linearized estimators

  Pierre Nodet, Thomas George · 11 August 2026

  We adapt two classical statistical estimators for quantifying uncertainty to modern deep learning, in order to provide clearer insights into uncertainty attributable to two sources : aleatoric uncertainty, or locally scarce data. Our approach leverages recent advances in approximate Fisher Informati…

• Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fields

  Yupei Nie, Lei Wang, Jiasen Liu · 11 August 2026

  Forward uncertainty propagation in complex physical systems can induce structured covariance across field-valued outputs. For a probabilistic surrogate, the total predictive covariance comprises the covariance of conditional means across input realizations and the average conditional predictive cova…

• A Unified Risk View of Uncertainty: Posterior Risk for Disentanglement and Evaluation Beyond Proxies

  Frieder Wizgall, Georg Tirpitz, Moritz Seiler, Kerstin Ritter, B\'alint Mucs\'anyi · 7 August 2026

  Reliable uncertainty estimates are critical in safety-sensitive applications, where understanding the sources of predictive uncertainty is essential. This often requires disentangling epistemic uncertainty from aleatoric uncertainty, yet these uncertainty types are not defined consistently across th…

• Stochastic Emulation using Generalized Stratified Sampling for Performance-Based Risk Optimization of Structures

  Isabela D. Rodrigues, Seymour M. J. Spence, Henrique M. Kroetz, Andr\'e T. Beck · 6 August 2026

  Metamodels are instrumental in reducing the computational burden associated with nested reliability analyses and optimization loops in Performance-Based Risk Optimization (PBRO) of structures under stochastic loads. In this context, stochastic emulators are particularly useful because they approxima…