FLASHμ: Fast Localizing And Sizing of Holographic Microparticles

Reconstructing the 3D location and size of microparticles from diffraction images - holograms - is a computationally expensive inverse problem that has traditionally been solved using physics-based reconstruction methods. More recently, researchers have used machine learning methods to speed up the process. However, for small particles in large sample volumes the performance of these methods falls short of standard physics-based reconstruction methods. Here we designed a two-stage neural network architecture, FLASH$\mu$, to detect small particles (6-100$\mu$m) from holograms with large sample depths up to 20cm. Trained only on synthetic data with added physical noise, our method reliably detects particles of at least 9$\mu$m diameter in real holograms, comparable to the standard reconstruction-based approaches while operating on smaller crops, at quarter of the original resolution and providing roughly a 600-fold speedup. In addition to introducing a novel approach to a non-local object detection or signal demixing problem, our work could enable low-cost, real-time holographic imaging setups.

Advancing Solutions for the Three-Body Problem Through Physics-Informed Neural Networks

First formulated by Sir Isaac Newton in his work "Philosophiae Naturalis Principia Mathematica", the concept of the Three-Body Problem was put forth as a study of the motion of the three celestial bodies within the Earth-Sun-Moon system. In a generalized definition, it seeks to predict the motion for an isolated system composed of three point masses freely interacting under Newton's law of universal attraction. This proves to be analogous to a multitude of interactions between celestial bodies, and thus, the problem finds applicability within the studies of celestial mechanics. Despite numerous attempts by renowned physicists to solve it throughout the last three centuries, no general closed-form solutions have been reached due to its inherently chaotic nature for most initial conditions. Current state-of-the-art solutions are based on two approaches, either numerical high-precision integration or machine learning-based. Notwithstanding the breakthroughs of neural networks, these present a significant limitation, which is their ignorance of any prior knowledge of the chaotic systems presented. Thus, in this work, we propose a novel method that utilizes Physics-Informed Neural Networks (PINNs). These deep neural networks are able to incorporate any prior system knowledge expressible as an Ordinary Differential Equation (ODE) into their learning processes as a regularizing agent. Our findings showcase that PINNs surpass current state-of-the-art machine learning methods with comparable prediction quality. Despite a better prediction quality, the usability of numerical integrators suffers due to their prohibitively high computational cost. These findings confirm that PINNs are both effective and time-efficient open-form solvers of the Three-Body Problem that capitalize on the extensive knowledge we hold of classical mechanics.