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.