Session W56: Model-based Statistical Physics, Computable Data, and Model-Free Artificial Intelligence

On the use of physics in machine learning for imaging and quantifying complex processes

We discuss the use of machine learning kernels as regularizers in problems of quantitative imaging and estimation for complex processes. In such problems, the “image” is not a final goal; it is rather an intermediate step toward estimating parameter values.

 

Recently, we have investigated laser speckle as an encoder for dynamics of interacting particulates. For instance, we developed a real-time method, the Physics Enhanced Auto Correlation Estimator (Peace) [1] which explicitly maps the probability density function of particle sizes (also referred to as particle size distribution, PSD) to the intensity autocorrelation of the speckle. After recording the speckle and computing its autocorrelation, a machine learning-aided decoder returns the PSD. It is important to note that this is a far-field, or “non-imaging” method—the interpretation of speckle as an encoder obviates the need to image individual particles. Instead, the ensemble statistical properties are obtained directly from the autocorrelation.

 

In this talk, we will discuss more extensively the quantitative properties of dynamic Peace, i.e. when the particle size distribution itself is evolving due to chemical or mechanical interactions. We will also discuss some preliminary work on the application of quantitative speckle to two novel domains: scattering from biological cells and the phloem in plants. In both cases, the speckle is interpreted as an encoder of diffusion, transport and reactive processes. These may only be partially explained from first principles, whereas the constitutive relationships necessarily need to be derived from the data.

 

[1] Qihang Zhang, et al, Nature Comm. 14:1159, 2023.

 

    

Energy Frontier Exploration using Particle Physics and AI

Artificial Intelligence (AI) and machine learning (ML) methods have proven to be powerful tools for the exploration of physics at the energy frontier of particle physics. Their expanding role in fundamental physics is driven by the challenges of increasingly large and complex data from experiments and computationally expensive simulations required to model and interpret the data, in addition to the rapid development of more powerful AI/ML tools for science-driven data exploration and interpretation. Moreover, exploiting symmetries inherent in physics data have inspired physics-informed ML as a vibrant sub-field of computer science research. I In this talk, I will provide a brief overview of key applications of AI/ML to fundamental physics research at the energy frontier of particle physics and describe several future directions in areas including explainable AI, uncertainty quantification, anomaly detection and real-time AI systems that will significantly enhance the scientific capabilities and opportunities of future experiments. Finally, I will briefly touch on how we are entering a new era in the relationship between AI and science and how scientists will need to learn how to navigate in this new environment.   

Data-driven medical image formation without a priori models

Elastograms are 3-D images of tissue mechanical properties constructed from a sparse set of force-displacement measurements recorded using ultrasonic imaging.  They can be an important medical resource if we can solve a difficult ill-posed inverse problem. The usual solution is to assume a parametric constitutive model of mechanical behavior and constrain the experiment to reduce model dimensionality until it matches the available data.  A better approach is to enter the sparse measurements into two finite-element algorithms (FEAs) operating on one meshed volume of the deformed medium.  One FEA operates on measured forces and the other on measured displacements, each modeling the deformation patterns based on the data they receive and an initial guess at material properties.  We replace the constitutive matrix that FEA depends on for material properties with initialized neural networks that iteratively learn those properties by training with data gathered after each FEA cycle.  The FEA models agree once both converge to the true medium properties.  This approach relies only on the measurements and the principles of equilibrium and compatibility imposed by the FEAs on the data when training the networks.  In this way, training occurs without assuming a constitutive model of material properties, making it ideal for model discovery. 

 

The neural networks learn material properties from sparse ultrasound measurements because every estimate of displacement made within a slowly deformed tissue contains information about the properties and boundary conditions throughout the entire contiguous medium.  As an operator probes tissues and numerical model development begins, an entropy-based measure of data diversity indicates to the operator when sufficient information has been collected.  Once a numerical model has converged, a constitutive model is applied to it to estimate parametric images for medical diagnosis.  Unlike deep learning methods that require training data spanning any object that might be encountered, this method focuses on collecting a comprehensive data set for a given patient.  We aim to discover what constitutes the comprehensive data set that informs machine learning for high-quality image formation.    

The Restricted Boltzmann Machine: from the statistical physics of disordered systems to a practical and interpretative generative machine learning.

In this talk I will present our recent work on the Restricted Boltzmann Machine (RBM). RBMs were introduced decades ago by Hinton as a variant of the Boltzmann Machine (BM), but with hidden variables and a characteristic bipartite architecture. RBMs, introduced at the time as a "product of experts", were successfully trained as a generative model using the so-called contrastive-divergence method and, despite their shallow and simple architecture, were able to generate convincing new samples for complex real-world datasets. They later became popular as building blocks for pre-trained deep neural networks before the advent of more sophisticated methods.

The increasing interest of physicists and statistical physicists in RBMs in recent years is driven to several factors. First, RBMs can be seen as a generalization of BM that can be used to study interesting emerging phenomena, such as the phase diagram of the learned machine, how the learned free energy landscape is related to the properties of the dataset, or how the features of the dataset are encoded during the learning dynamics. Secondly, its practicality and simplicity make it an accessible model for physicists, providing a more understandable alternative to large, opaque neural networks.

I will present our understanding of the phase diagram and the learning dynamics of this model at both analytical and numerical levels. I will then show how we can construct equivalences between RBMs and generalized BMs where the weights of the RBM can be mapped into effective K-body interactions so that we are able to infer interacting components for a given dataset.