BZPEERReading, trust and collaboration for research
Menu

Discover

GraphFollow connections around a paper, topic or saved view.

Workspaces

HomePick up where your research flow left off.InboxHandle requests, replies and notifications from one place.CollectionsCurate reading lists, evidence sets and shareable dossiers.ResearchSee your private provenance graph, trail and imports.CollaborationMove from discovery into focused discussion rooms.PublishDraft, preview and publish full-text research articles.

Network

ExpertsFind specialists worth following or asking for help.CommunitiesJoin research circles organized around shared work.PartnersSee external organizations active around the same topics.

Opportunities

ListingsBrowse roles, calls and collaborations with clearer fit signals.

Account

Log inReturn to your reading and collaboration workspace.Create accountStart saving work, following people and joining teams.
Log inCreate account

Researcher profile

Benjamin Peherstorfer

Benjamin Peherstorfer contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.NANumerical AnalysisMachine Learningphysics.comp-phphysics.plasm-phMethodology

Trust snapshot

Quick read

Trust 21 - EmergingVerification L1Unclaimed author
9works
0followers
6topics
4close collaborators

Actions

Decide how to stay connected

Follow researcher0

Identity and collaboration

How to connect with this researcher

Claiming links this public author record to a researcher profile and unlocks direct collaboration workflows.

Log in to claim

Direct collaboration

Open a focused conversation when the fit is right

Claim this author entity first to unlock direct invitations.

Research graph

See the researcher in context

Open full explorer

Inspect adjacent work, topics, institutions and collaborators without jumping out to a separate graph page.

Building this graph slice

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

9 published item(s)

preprint2026arXiv

A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions

Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We interpret this non-uniqueness as a gauge freedom: nullspace directions that leave the time derivative unchanged can be used to select better-conditioned parameter velocities. Building on Onsager's minimum-dissipation principle, we introduce a history variable -- interpretable as momentum -- and inject it only along the nullspace directions. The resulting Dirac-Frenkel-Onsager dynamics preserve instantaneous residual minimization, in contrast to standard regularization that can introduce bias, while promoting temporally smooth parameter evolutions. Examples demonstrate that the approach leads to increased robustness in singular and near-singular regimes.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization

This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta estimators are particularly efficient within outer-loop applications when the input distribution of the uncertainties changes during the outer loop, which is often the case in reliability-based design and shape optimization. We derive asymptotic bounds of the variance reduction of the meta estimators in the limit of convergence of the outer-loop results. We demonstrate the meta estimators, using data-driven surrogate models and biasing densities, on a design problem under uncertainty motivated by magnetic confinement fusion, namely the optimization of stellarator coil designs to maximize the estimated confinement of energetic particles. The meta estimators outperform all of their constituent variance reduction techniques alone, ultimately yielding two orders of magnitude speedup compared to standard Monte Carlo estimation at the same computational budget.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Accelerating the estimation of energetic particle confinement statistics in stellarators using multifidelity Monte Carlo

In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard Monte Carlo studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply multifidelity Monte Carlo to the study of energetic particle confinement in a 4-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with multifidelity Monte Carlo compared to standard Monte Carlo.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems

Classical reduced models are low-rank approximations using a fixed basis designed to achieve dimensionality reduction of large-scale systems. In this work, we introduce reduced deep networks, a generalization of classical reduced models formulated as deep neural networks. We prove depth separation results showing that reduced deep networks approximate solutions of parametrized hyperbolic partial differential equations with approximation error $ε$ with $\mathcal{O}(|\log(ε)|)$ degrees of freedom, even in the nonlinear setting where solutions exhibit shock waves. We also show that classical reduced models achieve exponentially worse approximation rates by establishing lower bounds on the relevant Kolmogorov $N$-widths.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

We present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system's governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh-Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Manifold Approximations via Transported Subspaces: Model reduction for transport-dominated problems

This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as hyperbolic conservation laws typically exhibit nonlinear structures, which means that traditional model reduction methods based on linear approximations are inefficient when applied to these problems. In contrast, the approach introduced in this work derives reduced approximations that are nonlinear by explicitly composing global transport dynamics with locally linear approximations of the solution manifolds. A time-stepping scheme evolves the nonlinear reduced models by transporting local approximation spaces along the characteristic curves of the governing equations. The proposed computational procedure allows an offline/online decomposition and is online-efficient in the sense that the complexity of accurately time-stepping the nonlinear reduced model is independent of that of the full model. Numerical experiments with transport through heterogeneous media and the Burgers' equation show orders of magnitude speedups of the proposed nonlinear reduced models based on transported subspaces compared to traditional linear reduced models and full models.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Model reduction for transport-dominated problems via online adaptive bases and adaptive sampling

This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these transport-dominated problems because propagating coherent structures typically introduce high-dimensional features that require high-dimensional approximation spaces. The approach proposed in this work exploits the locality in space and time of propagating coherent structures to derive efficient reduced models. Full-model solutions are approximated locally in time via local reduced spaces that are adapted with basis updates during time stepping. The basis updates are derived from querying the full model at a few selected spatial coordinates. A core contribution of this work is an adaptive sampling scheme for selecting at which components to query the full model to compute basis updates. The presented analysis shows that, in probability, the more local the coherent structure is in space, the fewer full-model samples are required to adapt the reduced basis with the proposed adaptive sampling scheme. Numerical results on benchmark examples with interacting wave-type structures and time-varying transport speeds and on a model combustor of a single-element rocket engine demonstrate the wide applicability of the proposed approach and runtime speedups of up to one order of magnitude compared to full models and traditional reduced models.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. The computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Stability of discrete empirical interpolation and gappy proper orthogonal decomposition with randomized and deterministic sampling points

This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction and state field approximation from measurements. Empirical interpolation derives approximations from a few samples (measurements) via interpolation in low-dimensional spaces. It has been observed that empirical interpolation can become unstable if the samples are perturbed due to, e.g., noise, turbulence, and numerical inaccuracies. The main contribution of this work is a probabilistic analysis that shows that stable approximations are obtained if samples are randomized and if more samples than dimensions of the low-dimensional spaces are used. Oversampling, i.e., taking more sampling points than dimensions of the low-dimensional spaces, leads to approximations via regression and is known under the name of gappy proper orthogonal decomposition. Building on the insights of the probabilistic analysis, a deterministic sampling strategy is presented that aims to achieve lower approximation errors with fewer points than randomized sampling by taking information about the low-dimensional spaces into account. Numerical results of reconstructing velocity fields from noisy measurements of combustion processes and model reduction in the presence of noise demonstrate the instability of empirical interpolation and the stability of gappy proper orthogonal decomposition with oversampling.

0 citations0 reviewsNo code linkedOpen access