arXiv subjects

Gert-Jan Both

Publications and source records attributed to Gert-Jan Both.

12 recordsLinked to original sources

arXiv2025

Revisiting PSF models: unifying framework and high-performance implementation

Localization microscopy often relies on detailed models of point spread functions. For applications such as deconvolution or PSF engineering, accurate models for light propagation in imaging systems with high numerical aperture are required. Different models have been proposed based on 2D Fourier transforms or 1D Bessel integrals. The most precise ones combine a vectorial description of the electric field and precise aberration models. However, it may be unclear which model to choose, as there is no comprehensive comparison between the Fourier and Bessel approaches yet. Moreover, many existing libraries are written in Java (e.g. our previous PSF generator software) or MATLAB, which hinders the integration into deep learning algorithms. In this work, we start from the original Richards-Wolf integral and revisit both approaches in a systematic way. We present a unifying framework in which we prove the equivalence between the Fourier and Bessel strategies and detail a variety of correction factors applicable to both of them. Then, we provide a high-performance implementation of our theoretical framework in the form of an open-source library that is built on top of PyTorch, a popular library for deep learning. It enables us to benchmark the accuracy and computational speed of different models, thus allowing for an in-depth comparison of the existing models for the first time. We show that the Bessel strategy is optimal for axisymmetric beams while the Fourier approach can be applied to more general scenarios. Our work enables efficient PSF computation on CPU or GPU, which can then be included in simulation and optimization pipelines.

physics.optics↗

arXiv2024

Rearrangement of single atoms in a 2000-site optical tweezers array at cryogenic temperatures

We report on the trapping of single rubidium atoms in large arrays of optical tweezers comprising up to 2088 sites in a cryogenic environment at 6 K. Our approach relies on the use of microscope objectives that are in-vacuum but at room temperature, in combination with windowless thermal shields into which the objectives are protruding to ensure a cryogenic environment for the trapped atoms. To achieve enough optical power for efficient trapping, we combine two lasers at slightly different wavelengths. We discuss the performance and limitations of our design. Finally, we demonstrate atom-by-atom rearrangement of an 828-atom target array using moving optical tweezers controlled by a field-programmable gate array.

physics.atom-ph↗

arXiv2024

Quantum-Enhanced Neural Exchange-Correlation Functionals

Kohn-Sham Density Functional Theory (KS-DFT) provides the exact ground state energy and electron density of a molecule, contingent on the as-yet-unknown universal exchange-correlation (XC) functional. Recent research has demonstrated that neural networks can efficiently learn to represent approximations to that functional, offering accurate generalizations to molecules not present during the training process. With the latest advancements in quantum-enhanced machine learning (ML), evidence is growing that Quantum Neural Network (QNN) models may offer advantages in ML applications. In this work, we explore the use of QNNs for representing XC functionals, enhancing and comparing them to classical ML techniques. We present QNNs based on differentiable quantum circuits (DQCs) as quantum (hybrid) models for XC in KS-DFT, implemented across various architectures. We assess their performance on 1D and 3D systems. To that end, we expand existing differentiable KS-DFT frameworks and propose strategies for efficient training of such functionals, highlighting the importance of fractional orbital occupation for accurate results. Our best QNN-based XC functional yields energy profiles of the H$_2$ and planar H$_4$ molecules that deviate by no more than 1 mHa from the reference DMRG and FCI/6-31G results, respectively. Moreover, they reach chemical precision on a system, H$_2$H$_2$, not present in the training dataset, using only a few variational parameters. This work lays the foundation for the integration of quantum models in KS-DFT, thereby opening new avenues for expressing XC functionals in a differentiable way and facilitating computations of various properties.

quant-ph↗

arXiv2024

Qadence: a differentiable interface for digital-analog programs

Digital-analog quantum computing (DAQC) is an alternative paradigm for universal quantum computation combining digital single-qubit gates with global analog operations acting on a register of interacting qubits. Currently, no available open-source software is tailored to express, differentiate, and execute programs within the DAQC paradigm. In this work, we address this shortfall by presenting Qadence, a high-level programming interface for building complex digital-analog quantum programs developed at Pasqal. Thanks to its flexible interface, native differentiability, and focus on real-device execution, Qadence aims at advancing research on variational quantum algorithms built for native DAQC platforms such as Rydberg atom arrays.

quant-ph↗

arXiv2021

Discovering PDEs from Multiple Experiments

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters, initial and boundary conditions that cannot be simply averaged out. We introduce a randomised adaptive group Lasso sparsity estimator to promote grouped sparsity and implement it in a deep learning based PDE discovery framework. It allows to create a learning bias that implies the a priori assumption that all experiments can be explained by the same underlying PDE terms with potentially different coefficients. Our experimental results show more generalizable PDEs can be found from multiple highly noisy datasets, by this grouped sparsity promotion rather than simply performing independent model discoveries.

stat.ML↗

arXiv2021

Fully differentiable model discovery

Model discovery aims at autonomously discovering differential equations underlying a dataset. Approaches based on Physics Informed Neural Networks (PINNs) have shown great promise, but a fully-differentiable model which explicitly learns the equation has remained elusive. In this paper we propose such an approach by integrating neural network-based surrogates with Sparse Bayesian Learning (SBL). This combination yields a robust model discovery algorithm, which we showcase on various datasets. We then identify a connection with multitask learning, and build on it to construct a Physics Informed Normalizing Flow (PINF). We present a proof-of-concept using a PINF to directly learn a density model from single particle data. Our work expands PINNs to various types of neural network architectures, and connects neural network-based surrogates to the rich field of Bayesian parameter inference.

stat.ML↗

arXiv2021

Sparsistent Model Discovery

Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model discovery algorithms based on sparse regression can actually recover the underlying physical processes. In this work, we show the design matrices used to infer the equations by sparse regression can violate the irrepresentability condition (IRC) of the Lasso, even when derived from analytical PDE solutions (i.e. without additional noise). Sparse regression techniques which can recover the true underlying model under violated IRC conditions are therefore required, leading to the introduction of the randomised adaptive Lasso. We show once the latter is integrated within the deep learning model discovery framework DeepMod, a wide variety of nonlinear and chaotic canonical PDEs can be recovered: (1) up to $\mathcal{O}(2)$ higher noise-to-sample ratios than state-of-the-art algorithms, (2) with a single set of hyperparameters, which paves the road towards truly automated model discovery.

stat.ML↗

arXiv2021

Sparsely constrained neural networks for model discovery of PDEs

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model discovery to densely sampled data-sets with low noise. Neural network-based approaches circumvent this limit by constructing a surrogate model of the data, but have to date ignored advances in sparse regression algorithms. In this paper we present a modular framework that dynamically determines the sparsity pattern of a deep-learning based surrogate using any sparse regression technique. Using our new approach, we introduce a new constraint on the neural network and show how a different network architecture and sparsity estimator improve model discovery accuracy and convergence on several benchmark examples. Our framework is available at \url{https://github.com/PhIMaL/DeePyMoD}

cs.LG↗

arXiv2021

Model discovery in the sparse sampling regime

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled observations. In this work, we investigate how deep learning can improve model discovery of partial differential equations when the spacing between sensors is large and the samples are not placed on a grid. We show how leveraging physics informed neural network interpolation and automatic differentiation, allow to better fit the data and its spatiotemporal derivatives, compared to more classic spline interpolation and numerical differentiation techniques. As a result, deep learning-based model discovery allows to recover the underlying equations, even when sensors are placed further apart than the data's characteristic length scale and in the presence of high noise levels. We illustrate our claims on both synthetic and experimental data sets where combinations of physical processes such as (non)-linear advection, reaction, and diffusion are correctly identified.

physics.comp-ph↗

arXiv2021

DeepMoD: Deep learning for Model Discovery in noisy data

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their derivatives. A neural network approximates the data and constructs the function library, but it also performs the sparse regression. This construction makes it extremely robust to noise, applicable to small data sets, and, contrary to other deep learning methods, does not require a training set. We benchmark our approach on several physical problems such as the Burgers', Korteweg-de Vries and Keller-Segel equations, and find that it requires as few as $\mathcal{O}(10^2)$ samples and works at noise levels up to $75\%$. Motivated by these results, we apply DeepMoD directly on noisy experimental time-series data from a gel electrophoresis experiment and find that it discovers the advection-diffusion equation describing this system.

physics.comp-ph↗

arXiv2019

Temporal Normalizing Flows

Analyzing and interpreting time-dependent stochastic data requires accurate and robust density estimation. In this paper we extend the concept of normalizing flows to so-called temporal Normalizing Flows (tNFs) to estimate time dependent distributions, leveraging the full spatio-temporal information present in the dataset. Our approach is unsupervised, does not require an a-priori characteristic scale and can accurately estimate multi-scale distributions of vastly different length scales. We illustrate tNFs on sparse datasets of Brownian and chemotactic walkers, showing that the inclusion of temporal information enhances density estimation. Finally, we speculate how tNFs can be applied to fit and discover the continuous PDE underlying a stochastic process.

physics.comp-ph↗

arXiv2017

Impact of Interaction Range and Curvature on Crystal Growth of Particles Confined to Spherical Surfaces

When colloidal particles form a crystal phase on a spherical template, their packing is governed by the effective interaction between them and the elastic strain of bending the growing crystal. For example, if growth commences under appropriate conditions, and the circular crystal that forms reaches a critical size, growth continues by incorporation of defects to alleviate elastic strain. Recently it was found experimentally that, if defect formation is somehow not possible, the crystal instead continues growing in ribbons that protrude from the original crystal. Here we report on computer simulations in which we observe both the formation of ribbons at short interaction ranges and packings that incorporate defects if the interaction is longer-ranged. The ribbons only form above some critical crystal size, below which the nucleus is roughly spherically shaped. We find that the scaling of the critical crystal size differs slightly from the one proposed by the Manoharan group, and reason this is because the actual process is a two-step heterogeneous nucleation of ribbons on top of roughly circular crystals.

cond-mat.soft↗