Learning Complexity to Guide Light-Induced Self-Organized Nanopatterns.

Ultrafast laser irradiation can induce spontaneous self-organization of surfaces into dissipative structures with nanoscale reliefs. These surface patterns emerge from symmetry-breaking dynamical processes that occur in Rayleigh-Bénard-like instabilities. In this study, we demonstrate that the coexistence and competition between surface patterns of different symmetries in two dimensions can be numerically unraveled using the stochastic generalized Swift-Hohenberg model. We originally propose a deep convolutional network to identify and learn the dominant modes that stabilize for a given bifurcation and quadratic model coefficients. The model is scale-invariant and has been calibrated on microscopy measurements using a physics-guided machine learning strategy. Our approach enables the identification of experimental irradiation conditions for a desired self-organization pattern. It can be generally applied to predict structure formation in situations where the underlying physics can be approximately described by a self-organization process and data is sparse and nontime series. Our Letter paves the way for supervised local manipulation of matter using timely controlled optical fields in laser manufacturing.

Learning PDE to Model Self-Organization of Matter.

A self-organization hydrodynamic process has recently been proposed to partially explain the formation of femtosecond laser-induced nanopatterns on Nickel, which have important applications in optics, microbiology, medicine, etc. Exploring laser pattern space is difficult, however, which simultaneously (i) motivates using machine learning (ML) to search for novel patterns and (ii) hinders it, because of the few data available from costly and time-consuming experiments. In this paper, we use ML to predict novel patterns by integrating partial physical knowledge in the form of the Swift-Hohenberg (SH) partial differential equation (PDE). To do so, we propose a framework to learn with few data, in the absence of initial conditions, by benefiting from background knowledge in the form of a PDE solver. We show that in the case of a self-organization process, a feature mapping exists in which initial conditions can safely be ignored and patterns can be described in terms of PDE parameters alone, which drastically simplifies the problem. In order to apply this framework, we develop a second-order pseudospectral solver of the SH equation which offers a good compromise between accuracy and speed. Our method allows us to predict new nanopatterns in good agreement with experimental data. Moreover, we show that pattern features are related, which imposes constraints on novel pattern design, and suggest an efficient procedure of acquiring experimental data iteratively to improve the generalization of the learned model. It also allows us to identify the limitations of the SH equation as a partial model and suggests an improvement to the physical model itself.

Predicting Laser-Induced Colors of Random Plasmonic Metasurfaces and Optimizing Image Multiplexing Using Deep Learning.

Structural colors of plasmonic metasurfaces have been promised to a strong technological impact thanks to their high brightness, durability, and dichroic properties. However, fabricating metasurfaces whose spatial distribution must be customized at each implementation and over large areas is still a challenge. Since the demonstration of printed image multiplexing on quasi-random plasmonic metasurfaces, laser processing appears as a promising technology to reach the right level of accuracy and versatility. The main limit comes from the absence of physical models to predict the optical properties that can emerge from the laser processing of metasurfaces in which random metallic nanostructures are characterized by their statistical properties. Here, we demonstrate that deep neural networks trained from experimental data can predict the spectra and colors of laser-induced plasmonic metasurfaces in various observation modes. With thousands of experimental data, produced in a rapid and efficient way, the training accuracy is better than the perceptual just noticeable change. This accuracy enables the use of the predicted continuous color charts to find solutions for printing multiplexed images. Our deep learning approach is validated by an experimental demonstration of laser-induced two-image multiplexing. This approach greatly improves the performance of the laser-processing technology for both printing color images and finding optimized parameters for multiplexing. The article also provides a simple mining algorithm for implementing multiplexing with multiple observation modes and colors from any printing technology. This study can improve the optimization of laser processes for high-end applications in security, entertainment, or data storage.

Iterative multilinear optimization for planar model fitting under geometric constraints.

Planes are the core geometric models present everywhere in the three-dimensional real world. There are many examples of manual constructions based on planar patches: facades, corridors, packages, boxes, etc. In these constructions, planar patches must satisfy orthogonal constraints by design (e.g. walls with a ceiling and floor). The hypothesis is that by exploiting orthogonality constraints when possible in the scene, we can perform a reconstruction from a set of points captured by 3D cameras with high accuracy and a low response time. We introduce a method that can iteratively fit a planar model in the presence of noise according to three main steps: a clustering-based unsupervised step that builds pre-clusters from the set of (noisy) points; a linear regression-based supervised step that optimizes a set of planes from the clusters; a reassignment step that challenges the members of the current clusters in a way that minimizes the residuals of the linear predictors. The main contribution is that the method can simultaneously fit different planes in a point cloud providing a good accuracy/speed trade-off even in the presence of noise and outliers, with a smaller processing time compared with previous methods. An extensive experimental study on synthetic data is conducted to compare our method with the most current and representative methods. The quantitative results provide indisputable evidence that our method can generate very accurate models faster than baseline methods. Moreover, two case studies for reconstructing planar-based objects using a Kinect sensor are presented to provide qualitative evidence of the efficiency of our method in real applications.