Session P61: Data Science for Dynamical Systems and Real World Networks

Live

Research in machine learning is rapidly branching into the physical sciences, with a particular focus on dynamical systems and control. There are a number of pressing challenges in modern dynamical systems that stand to benefit from these efforts. First, many systems of interest do not have known dynamics, and dynamical systems models must be discovered from data; even systems where we have governing equations, such as turbulence, are too complex to analyze and control, motivating reduced-order models. Second, it is important to discover new coordinate systems where the dynamics are simplified. Third, physical systems often have symmetries and conservation laws that may be enforced in the learning process. In this talk, we will discuss several deep learning approaches to simultaneously discover coordinate transformations and parsimonious models of the dynamics. We will put a premium on models that are generalizable and interpretable, and will demonstrate how to bake in partially known physics. These ideas will be motivated on examples in fluid dynamics.   

Live

Small-world networks are characterized by highly clustered nodes and a small characteristic path length. They appear in various contexts; notable examples include biological systems such as neural networks and societal infrastructure such as airport networks. Since their identification in 1998 by Watts and Strogatz, small-world networks have been studied with numerous qualitative and quantitative measures. Traditional methods of identifying whether or not a network is a small-world rely on comparisons between its characteristic path length and local cliquishness with values for a purely random or purely regular graph of the same dimensions. The effectiveness of each of these measures is highly dependent on the specific aspects of a small-world network of interest in a given context. Here we present a practical tool to verify whether a network can be considered a small-world based on its eigenvalue spectrum properties. We introduce an ensemble of small-world matrices and apply the Rogers-Pastur formula for computing the spectra of non-Hermitian matrices. Next, we analyze the spectra's main features and compare our results to other common measures employed to describe small-world networks. Finally, we illustrate our results on several well-known examples of small-world networks.   

Live

I will discuss several ways in which machine learning can be used for solving and understanding the solutions of nonlinear partial differential equations. Part of the talk will focus on learning discretizations for coarse graining the numerical solutions of the Navier Stokes equation. I will also discuss how learned representations can give insight into the nature of the solution manifold for the navier stokes equations, allowing the discovery of new classes of solutions.   

Live

The concept of Digital Twin originally came from the industry, which was referring to a “digital copy of the physical asset.” The ambitious attempt here is to construct a virtual laboratory infrastructure to solve a variety of technical challenges in data acquisition, control, analysis, and model-driven interpretation. The digital twin is expected to faithfully mimic facilities, including automated workflows with continuous updates from real experiments, which would eventually augment the experimentalists' decision making and execution of optimal experimental strategies to drive physical knowledge acquisition for user facilities. As daunting as it sounds, I will explain the challenges along with the milestones: 1) developing physically accurate quantum chemistry methods that improve the numerical accuracy of XPS binding energy (BE) calculation; 2) realizing that a central piece of chemical reaction network (CRN) is universal in the chemical systems of interest, such as reactors and heterogeneous catalysis 3) sharing a user-friendly, natural chemical language syntax Digital Twin v.01 software package, which we welcome collaboration and feedback in any form.   

Live

Stories of mega-jams that last tens of hours or even days appear not only in fiction but also in reality. In this context, it is important to characterize the collapse of the network, defined as the transition from a characteristic travel time to orders of magnitude longer for the same distance traveled. In this multicity study, we unravel this complex phenomenon under various conditions of demand and translate it to the travel time of the individual drivers. First, we start with the current conditions, showing that there is a characteristic time τ that takes a representative group of commuters to arrive at their destinations once their maximum density has been reached. While this time differs from city to city, it can be explained by Γ, defined as the ratio of the vehicle miles traveled to the total vehicle distance the road network can support per hour. Modifying Γ can improve τ and directly inform planning and infrastructure interventions.   

Live

Recent natural disasters have shown that urban road networks are susceptible to cascading failures as evidenced by city scale traffic jams. Further, the rise of internet connected vehicles and smart city infrastructure leads to the potential for hackers and nation states to target disruptions that maximize the potential for cascading failure. Here, we quantify the potential for targeted disruptions on urban traffic networks. Guided by microscopic traffic simulations, we develop a theoretical framework for predicting the growth in cascading traffic jams around disruptions. Application of our framework to previously validated Boston trips reveals that a targeted disruption of roads leads to a disproportionately large proportion of shortest time routes being blocked, due to the relative importance of a few key roads. We find that an initial targeted disruption quickly impacts a significant portion of incoming traffic. Depending on the percentage of initial disruption, vehicle density, and characteristic free flow trip time the cascade occurs on the minutes to hours timescale. However, connected component analysis reveals that route redundancy provides an order of magnitude improvement in fragility, demonstrating the potential for strengthening transportation against network failure.   

Live

The execution of machine learning (ML) algorithms largely depends on the computing `substrate', which is often not optimized for running ML tasks. The invention of ML-tailored hardware greatly improves the computing speed and power efficiency. Photonic devices are well suited for ML due to the parallelism of light. Here we utilize the complicated wave dynamics inside a chaotic-shaped overmoded electromagnetic cavity containing nonlinear elements to emulate the complex dynamics of the Reservoir Computer (RC). We propose unique techniques to create virtual RC nodes by both spectral and spatial perturbation. The computational power of the wave-based RC is experimentally demonstrated with the so-called Observer Task, where we predict the future evolution of chaotic Rossler y(t) and z(t) time series using the x(t) series as the input. Different tasks are executed with a single RC physical device by simply switching output couplers.   

On Demand

Natural selection drives species to develop brains, with sizes that increase with the complexity of the tasks to be tackled. Our goal is to investigate the balance between the metabolic costs of larger brains compared to the advantage they provide in solving general and combinatorial problems. Defining advantage as the performance relative to competitors, a two-player game based on the knapsack problem is used. Within this framework, two opponents compete over shared resources, with the goal of collecting more resources than the opponent. Neural networks of varying sizes are trained using a variant of the AlphaGo Zero* algorithm, by generating training data out of self play games. A surprisingly simple relation, N_A /(N_A+N_B), is found for the relative win rate of a net with N_A neurons against one with N_B . Success increases linearly with investments in additional resources when the networks sizes are very different, i.e. when N_A is much smaller than N_B , with returns diminishing when both networks become comparable in size.
References:
Silver, David, et al. "Mastering the game of go without human knowledge." nature 550.7676 (2017): 354-359.