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Ultra-intense lasers that ionize atoms and accelerate electrons in solids to near the speed of light can lead to kinetic instabilities that alter the laser absorption and subsequent electron transport, isochoric heating, and ion acceleration. These instabilities can be difficult to characterize, but X-ray scattering at keV photon energies allows for their visualization with femtosecond temporal resolution on the few nanometer mesoscale. Here, we perform such experiment on laser-driven flat silicon membranes that shows the development of structure with a dominant scale of 60 nm in the plane of the laser axis and laser polarization, and 95 nm in the vertical direction with a growth rate faster than 0.1 fs−1 . Combining the XFEL experiments with simulations provides a complete picture of the structural evolution of ultra-fast laser-induced plasma density development, indicating the excita- tion of plasmons and a filamentation instability. Particle-in-cell simulations confirm that these signals are due to an oblique two-stream filamentation instability. These findings provide new insight into ultra-fast instability and heating processes in solids under extreme conditions at the nanometer level with possible implications for laser particle acceleration, inertial confinement fusion, and laboratory astrophysics.

Understanding laser-solid interactions is important for the development of laser-driven particle and photon sources, e.g., tumor therapy, astrophysics, and fusion. Currently, these interactions can only be modeled by simulations that need to be verified experimentally. Consequently, pump-probe experiments were conducted to examine the laser-plasma interaction that occurs when a high intensity laser hits a solid target. Since we aim for a femtosecond temporal and nanometer spatial resolution at European XFEL, we employ Small-Angle X-ray Scattering (SAXS) and Phase Contrast Imaging (PCI) that can each be approximated by an analytical propagator. In our reconstruction of the target, we employ gradient descent (GD) to iteratively minimize the error between experimental and synthetic patterns propagated from proposed target structures. By implementing the propagator in PyTorch, we leverage the automatic differentiation and GPU acceleration for the GD fit and at the same time obtain a differentiable physically-based loss function for unsupervised training of inversion or surrogate models. For a classical fit, we sample many different initial values for parameters, such as target asymmetry, to find the global minimum, leveraging batch-parallelism. A data-driven model to predict initial conditions close to actual minima can be trained in an unsupervised manner using our pipeline.

Phase retrieval is an ill-posed inverse problem with several applications in the fields of medical imaging and materials science. Conventional phase retrieval algorithms either simplify the problem by assuming certain object properties and optical propagation regimes or tuning a large number of free parameters. While the latter most often leads to good solutions for a wider application range, it is still a time-consuming process, even for experienced users. One way to circumvent this is by introducing a self-optimizing machine learning- based algorithm. Basing this on invertible networks such as normalising flows ensures good inversion, effi- cient sampling, and fast probability density estimation for large images and generally, complex-valued dis- tributions. Here, complex wavefield datasets are trained and tested on a normalising flows-based machine learning model for phase retrieval called conditional Wavelet Flow (cWF) and benchmarked against other conventional algorithms and baseline models. The cWF algorithm adds a conditioning network on top of the Wavelet Flow algorithm that is able to model the conditional data distribution of high resolution images of up to 1024 x 1024 pixels, which was not possible in other flow-based models. Additionally, cWF takes advantage of the parallelized training of different image resolutions, allowing for more efficient and fast training of large datasets. The trained algorithm is then applied to X-ray holography data wherein fast and high-quality image reconstruction is made possible.

Understanding laser-solid interactions is important for the development of laser-driven particle and photon sources, e.g., tumor therapy, astrophysics, and fusion. Currently, these interactions can only be modeled by simulations that need to be verified experimentally. Consequently, pump-probe experiments were conducted to examine the laser-plasma interaction that occurs when a high intensity laser hits a solid target. Since we aim for a femtosecond temporal and nanometer spatial resolution at European XFEL, we employ Small-Angle X-ray Scattering (SAXS) and Phase Contrast Imaging (PCI) that can each be approximated by an analytical propagator. In our reconstruction of the target, we employ a gradient descent algorithm that iteratively minimizes the error between experimental and synthetic patterns propagated from proposed target structures. By implementing the propagator in PyTorch we leverage the automatic differentiation capabilities, as well as the speed-up by computing the process on a GPU. We perform a scan of different initial parameters to find the global minimum, which is accelerated by batching multiple parallel reconstructions.

In the exploration of universe and matter, dealing with inverse problems is often a central challenge. In many experimental investigations, which are carried out in particular at large-scale research facilities such as FRM II, DESY or European XFEL, the essential phase information in the experimental data is lost due to the measurement principle (phase problem). Therefore, methods based on direct inversion are not applicable, so that the solution of the underlying non-convex optimization problem is usually very time-consuming and expensive to implement. Here we present our project “Versatile Inverse Problem fRamework” (VIPR), recently funded by the Federal Ministry of Education and Research (Grant 05D23CJ1). The stated goal of our project is to develop a flexible software framework for data-driven solutions to inverse problems. First we plan to focus on using invertible neural networks. Other architectures can be also considered at later stages of the project. The main application areas envisioned include grazing incidence small- and wide-angle scattering with both neutrons and x-rays, neutron/x-ray reflectivity, and ptychography. Development will also take into account requirements from spectroscopy and particle physics.

Ultra-intense lasers that ionize and accelerate electrons in solids to near the speed of light can lead to kinetic instabilities that alter the laser absorption and subsequent electron transport, isochoric heating, and ion acceleration. These instabilities can be difficult to characterize, but a novel approach using X-ray scattering at keV energies allows for their visualization with femtosecond temporal resolution on the few nanometer mesoscale. Our experiments on laser-driven flat silicon membranes show the development of structure with a dominant scale of $~60\unit{nm}$ in the plane of the laser axis and laser polarization, and $~95\unit{nm}$ in the vertical direction with a growth rate faster than $0.1/\mathrm{fs}$. Combining the XFEL experiments with simulations provides a complete picture of the structural evolution of ultra-fast laser-induced instability development, indicating the excitation of surface plasmons and the growth of a new type of filamentation instability. These findings provide new insight into the ultra-fast instability processes in solids under extreme conditions at the nanometer level with important implications for inertial confinement fusion and laboratory astrophysics.

High-fidelity (computer-) experiments are very expensive to perform, hence extracting as much information as possible from the collected data is vital. We present methods to estimate experiment outcomes based on ingested past data, to steer further sample acquisition both by suggesting paths for maximized uncertainty reduction and highlighting sensitivities on inputs, with use-cases from laser-light propagation and laser-plasma interactions to electron-bunch kinetics.

Understanding laser-solid interactions is important for the development of laser-driven particle and photon sources, e.g., tumor therapy, astrophysics, and fusion. Currently, these interactions can only be modeled by simulations that need to be verified experimentally. Consequently, pump-probe experiments were conducted to examine the laser-plasma interaction that occurs when a high intensity laser hits a solid target. Since we aim for a femtosecond temporal and nanometer spatial resolution at European XFEL, we employ Small-Angle X-ray Scattering (SAXS) and Phase Contrast Imaging (PCI) that can each be approximated by an analytical propagator. In our reconstruction of the target, we employ a gradient descent algorithm that iteratively minimizes the error between experimental and synthetic patterns propagated from proposed target structures. By implementing the propagator in PyTorch we leverage the automatic differentiation capabilities, as well as the speed-up by computing the process on a GPU. We perform a scan of different initial parameters to find the global minimum, which is accelerated by batching multiple parallel reconstructions. The fully differentiable implementation of a forward function may serve as a physically-constraining loss, enabling training with unpaired data or unsupervised training of neural networks to predict the initial parameters for the gradient descent fit.

The understanding of laser-solid interactions is important to the development of future laser-driven particle and photon sources, e.g., for tumor therapy, astrophysics or fusion. Currently, these interactions can only be modeled by simulations which need verification in the real world. Consequently, in 2016, a pump-probe experiment was conducted by Thomas Kluge to examine the laser-plasma interaction that occurs when an ultrahigh-intensity laser hits a solid density target. To handle the nanometer spatial and femtosecond temporal resolution of the laser-plasma interactions, Small-Angle X-Ray Scattering (SAXS) was used as a diagnostic to reconstruct the laser-driven target. However, the reconstruction of the target from the SAXS diffraction pattern is an inverse problem which are often ambiguous and has no closed-form solution. We aim to simplify the process of reconstructing the target from SAXS images by employing Neural Networks due to their speed and generalization capabilities. To be more specific, we use a conditional Invertible Neural Network (cINN) to resolve the ambiguities with a probability density distribution. In consequence, the cINN is trained on simulated diffraction patterns and their respective ground truth parameters. The cINN is able to accurately reconstruct simulated- as well as preshot data. The performance on main-shot data remains unclear due to the fact that the simulation might not be able to explain the governing processes.

The understanding of laser-solid interactions is important to the development of future laser-driven particle and photon sources, e.g., for tumor therapy, astrophysics or fusion. Currently, these interactions can only be modeled by simulations which need verification in the real world. Consequently, in 2016, a pump-probe experiment was conducted by Thomas Kluge to examine the laser-plasma interaction that occurs when an ultrahigh-intensity laser hits a solid density target. To handle the nanometer spatial and femtosecond temporal resolution of the laser-plasma interactions, Small-Angle X-Ray Scattering (SAXS) was used as a diagnostic to reconstruct the laser-driven target. However, the reconstruction of the target from the SAXS diffraction pattern is an inverse problem which are often ambiguous, due to the phase problem, and has no closed-form solution. We aim to simplify the process of reconstructing the target from SAXS images by employing Neural Networks, due to their speed and generalization capabilities. To be more specific, we use a conditional Invertible Neural Network (cINN), a type ofNormalizing Flows, to resolve the ambiguities of the target with a probability density distribution. The target in this case is modelled by a simple grating function with three parameters. We chose this analytically well-defined and relatively simple target as a trial run for Neural Networks in this field to pave the way for more sophisticated targets and methods. Unfortunately, we don’t have enough and reliable experimental data that could be used as training. So, in consequence, the network is trained only on simulated diffraction patterns and their respective ground truth parameters. The cINN is able to accurately reconstruct simulated- as well as preshot data. The performance on main-shot data remains unclear due to the fact that the simulation might not be able to explain the governing processes.

The understanding of laser-solid interactions is important to the development of future laser-driven particle and photon sources, e.g., for tumor therapy, astrophysics or fusion. Currently, these interactions can only be modeled by simulations which need verification in the real world. Consequently, in 2016, a pump-probe experiment was conducted by Thomas Kluge to examine the laser-plasma interaction that occurs when an ultrahigh-intensity laser hits a solid density target. To handle the nanometer spatial and femtosecond temporal resolution of the laser-plasma interactions, Small-Angle X-Ray Scattering (SAXS) was used as a diagnostic to reconstruct the laser-driven target. However, the reconstruction of the target from the SAXS diffraction pattern is an inverse problem which are often ambiguous, due to the phase problem, and has no closed-form solution. We aim to simplify the process of reconstructing the target from SAXS images by employing Neural Networks, due to their speed and generalization capabilities. To be more specific, we use a conditional Invertible Neural Network (cINN), a type of Normalizing Flows, to resolve the ambiguities of the target with a probability density distribution. The target in this case is modelled by a simple grating function with three parameters. We chose this analytically well-defined and relatively simple target as a trial run for Neural Networks in this field to pave the way for more sophisticated targets and methods. Unfortunately, we don’t have enough and reliable experimental data that could be used as training. So, in consequence, the network is trained only on simulated diffraction patterns and their respective ground truth parameters. The cINN is able to accurately reconstruct simulated- as well as preshot data. The performance on main-shot data remains unclear due to the fact that the simulation might not be able to explain the governing processes.

This simulated dataset consists of 48k train, 6k validation and 6k test data in the h5py file format. A small example on how to access the data is located in the python script "load_data_example.py". "all_params.h5" are the three parameters of each grating in the order sigma, g, b. "all_dist.h5" are the gratings and "all_endproduct.h5" are the 2048D lineouts of the SAXS diffraction pattern. Besides the |FFT|^2 SAXS propagator a number of pertubations were implemented in order to close the domain gap between simulation and experiment.