Publications (33)
Ensuring Topological Data-Structure Preservation under Autoencoder Compression due to Latent Space Regularization in Gauss--Legendre nodes
Chethan Krishnamurthy Ramanaik, Juan-Esteban Suarez Cardona, Anna Willmann +3
We formulate a data independent latent space regularisation constraint for general unsupervised autoencoders. The regularisation rests on sampling the autoencoder Jacobian in Legen…
Interpolation in Polynomial Spaces of p-Degree
Phil-Alexander Hofmann, Damar Wicaksono, Michael Hecht
We recently introduced the Fast Newton Transform (FNT), an hierarchical algorithm for performing multivariate Newton interpolation in arbitrary downward closed polynomial spaces of…
Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes
Murad Alim, Babak Haghighat, Michael Hecht +3
Using wall-crossing formulae and the theory of mock modular forms we derive a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor…
A note on the rate of convergence of integration schemes for closed surfaces
Gentian Zavalani, Elima Shehu, Michael Hecht
In this paper, we issue an error analysis for integration over discrete surfaces using the surface parametrization presented in [PS22] as well as prove why even-degree polynomials…
Second roton feature in the strongly coupled electron liquid
Thomas M. Chuna, Jan Vorberger, Panagiotis Tolias +5
We present extensive \emph{ab initio} path integral Monte Carlo (PIMC) results for the dynamic properties of the finite temperature uniform electron gas (UEG) over a broad range of…
Replacing Automatic Differentiation by Sobolev Cubatures fastens Physics Informed Neural Nets and strengthens their Approximation Power
Juan Esteban Suarez Cardona, Michael Hecht
We present a novel class of approximations for variational losses, being applicable for the training of physics-informed neural nets (PINNs). The loss formulation reflects classic…
PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods
Alexander Benedix Robles, Phil-Alexander Hofmann, Thomas Chuna +2
Path integral Monte Carlo (PIMC) simulations are a cornerstone for studying quantum many-body systems. The analytic continuation (AC) needed to estimate dynamic quantities from the…
Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces
Sachin K. Thekke Veettil, Gentian Zavalani, Uwe Hernandez Acosta +2
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. T…
On Adversarial Vulnerability of Vision-Language Models through the Lens of Intermediate Spectral Subspaces
Chethan Krishnamurthy Ramanaik, Tobias Callies, Michael Hecht +1
Adversarial vulnerability in deep neural networks (DNNs) has been studied from the perspectives of decision-boundary geometry, feature robustness, input-output Jacobians, and the i…
Flat Connections in Open String Mirror Symmetry
Murad Alim, Michael Hecht, Hans Jockers +3
We study a flat connection defined on the open-closed deformation space of open string mirror symmetry for type II compactifications on Calabi-Yau threefolds with D-branes. We use…
The Variability of the Black-Hole Image in M87 at the Dynamical Time Scale
Kaushik Satapathy, Dimitrios Psaltis, Feryal Ozel +235
The black-hole images obtained with the Event Horizon Telescope (EHT) are expected to be variable at the dynamical timescale near their horizons. For the black hole at the center o…
High-order integration on regular triangulated manifolds reaches super-algebraic approximation rates through cubical re-parameterizations
Gentian Zavalani, Oliver Sander, Michael Hecht
We present a novel methodology for deriving high-order volume elements (HOVE) designed for the integration of scalar functions over regular embedded manifolds. For constructing HOV…
Multivariate Newton Interpolation
Michael Hecht, Karl B. Hoffmann, Bevan L. Cheeseman +1
For , and a given function , the polynomial interpolation problem (PIP) is to determine a unisolvent node…
Multivariate Newton Interpolation in Downward Closed Spaces Reaches the Optimal Geometric Approximation Rates for Bos--Levenberg--Trefethen Functions
Michael Hecht, Phil-Alexander Hofmann, Damar Wicaksono +5
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runti…
Roadmap on Deep Learning for Microscopy
Giovanni Volpe, Carolina Wählby, Lei Tian +72
Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasin…
Isomorphic chain complexes of Hamiltonian dynamics on tori
Michael Hecht
In this work we construct for a given smooth, generic Hamiltonian on the torus a chain isomorphism $ Φ_* : \big(C_*…
Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
Murad Alim, Michael Hecht, Hans Jockers +3
We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a g…
Tight Localizations of Feedback Sets
Michael Hecht, Krzysztof Gonciarz, Szabolcs Horvát
The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs or vertices who…
Multivariate Polynomial Regression of Euclidean Degree Extends the Stability for Fast Approximations of Trefethen Functions
Sachin K. Thekke Veettil, Yuxi Zheng, Uwe Hernandez Acosta +2
We address classic multivariate polynomial regression tasks from a novel perspective resting on the notion of general polynomial -degree, with total, Euclidean, and maximum de…
High-Angular-Resolution and High-Sensitivity Science Enabled by Beamformed ALMA
Vincent Fish, Walter Alef, James Anderson +66
An international consortium is presently constructing a beamformer for the Atacama Large Millimeter/submillimeter Array (ALMA) in Chile that will be available as a facility instrum…
Exact Localisations of Feedback Sets
Michael Hecht
The feedback arc (vertex) set problem, shortened FASP (FVSP), is to transform a given multi digraph into an acyclic graph by deleting as few arcs (vertices) as possible.…
Mitigating Numerical Stiffness in Least-Squares Formulations of Elliptic PDEs for Physics-Informed Neural Networks
Phil-Alexander Hofmann, Michael Hecht
We present theoretical insights into residual loss formulations of physics-informed neural networks (PINNs) for learning solutions of partial differential equations (PDEs)…
Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
Murad Alim, Michael Hecht, Hans Jockers +3
We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric G…
High-order numerical integration on regular embedded surfaces
Gentian Zavalani, Michael Hecht
We present a high-order surface quadrature (HOSQ) for accurately approximating regular surface integrals on closed surfaces. The initial step of our approach rests on exploiting sq…
Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
Tobias Dornheim, Damar C. Wicaksono, Juan E. Suarez-Cardona +5
We introduce an exact framework to compute the positive frequency moments of different dynamic properties from imaginary-time quantum Monte Ca…
Extinction and persistence criteria in non-local Klausmeier model of vegetation dynamics on flat landscapes
Maciej Tadej, Ricardo Martinez-Garcia, Michael Hecht
This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a fi…
InFlow: Robust outlier detection utilizing Normalizing Flows
Nishant Kumar, Pia Hanfeld, Michael Hecht +3
Normalizing flows are prominent deep generative models that provide tractable probability distributions and efficient density estimation. However, they are well known to fail while…
Hybrid Surrogate Models: Circumventing Gibbs Phenomenon for Partial Differential Equations with Finite Shock-Type Discontinuities
Juan-Esteban Suarez Cardona, Shashank Reddy, Michael Hecht
We introduce the concept of Hybrid Surrogate Models (HSMs) -- combining multivariate polynomials with Heavyside functions -- as approximates of functions with finitely many jump di…
Polynomial-Model-Based Optimization for Blackbox Objectives
Janina Schreiber, Damar Wicaksono, Michael Hecht
For a wide range of applications the structure of systems like Neural Networks or complex simulations, is unknown and approximation is costly or even impossible. Black-box optimiza…
Accelerating Multivariate Newton Interpolation in Downward Closed Polynomial Spaces
Phil-Alexander Hofmann, Michael Hecht
We introduce the fast Newton transform (FNT), a multivariate Newton interpolation algorithm for downward closed polynomial spaces in quasi-tensorial grids. The FNT computes the New…
PMBO: Enhancing Black-Box Optimization through Multivariate Polynomial Surrogates
Janina Schreiber, Pau Batlle, Damar Wicaksono +1
We introduce a surrogate-based black-box optimization method, termed Polynomial-model-based optimization (PMBO). The algorithm alternates polynomial approximation with Bayesian opt…
Multivariate Interpolation in Unisolvent Nodes -- Lifting the Curse of Dimensionality
Michael Hecht, Krzysztof Gonciarz, Jannik Michelfeit +2
We extend Newton and Lagrange interpolation to arbitrary dimensions. The core contribution that enables this is a generalized notion of non-tensorial unisolvent nodes, i.e., nodes…
Learning Partial Differential Equations by Spectral Approximates of General Sobolev Spaces
Juan-Esteban Suarez Cardona, Phil-Alexander Hofmann, Michael Hecht
We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we real…