Machine learning based data-driven discovery of nonlinear phase-field dynamics

One of the main questions regarding complex systems at large scales concerns the effective interactions and driving forces that emerge from the detailed microscopic properties. Coarse-grained models aim to describe complex systems in terms of coarse-scale equations with a reduced number of degrees of freedom. Recent developments in machine learning (ML) algorithms have significantly empowered the discovery process of the governing equations directly from data. However, it remains difficult to discover partial differential equations (PDEs) with high-order derivatives. In this paper, we present new data-driven architectures based on multi-layer perceptron (MLP), convolutional neural network (CNN), and a combination of CNN and long short-term memory (CNN-LSTM) structures for discovering the non-linear equations of motion for phase-field models with non-conserved and conserved order parameters. The well-known Allen--Cahn, Cahn--Hilliard, and the phase-field crystal (PFC) models were used as the test cases. Two conceptually different types of implementations were used: (a) guided by physical intuition (such as local dependence of the derivatives) and (b) in the absence of any physical assumptions (black-box model). We show that not only can we effectively learn the time derivatives of the field in both scenarios, but we can also use the data-driven PDEs to propagate the field in time and achieve results in good agreement with the original PDEs

Relaxation Redistribution Method for model reduction

The Relaxation Redistribution Method (RRM) is based on the notion of slow invariant manifold (SIM) and is applied for constructing a simplified model of detailed multiscale combustion phenomena. The RRM procedure can be regarded as an efficient and stable scheme for solving the film equation of dynamics, where a discrete set of points is gradually relaxed towards the slow invariant manifold (SIM). Here, the global realization of the RRM algorithm is briefly reviewed and used for auto-ignition and adiabatic premixed laminar flame of a homogeneous hydrogen-air ideal gas mixture

The global relaxation redistribution method for reduction of combustion kinetics

An algorithm based on the Relaxation Redistribution Method (RRM) is proposed for constructing the Slow Invariant Manifold (SIM) of a chosen dimension to cover a large fraction of the admissible composition space that includes the equilibrium and the initial state. The manifold boundaries are determined with the help of the Rate Controlled Constrained Equilibrium (RCCE) method, which also provides the initial guess for the SIM. The latter is iteratively refined until convergence and the converged manifold is tabulated. A criterion based on the departure from invariance is proposed to find the region over which the reduced description is valid. The global realization of the RRM algorithm is applied to constant pressure auto-ignition and adiabatic premixed laminar flames of hydrogen-air mixture

Novel tool to quantify with single-cell resolution the number of incoming AAV genomes co-expressed in the mouse nervous system.

Adeno-associated viral (AAV) vectors are an established and safe gene delivery tool to target the nervous system. However, the payload capacity of <4.9 kb limits the transfer of large or multiple genes. Oversized payloads could be delivered by fragmenting the transgenes into separate AAV capsids that are then mixed. This strategy could increase the AAV cargo capacity to treat monogenic, polygenic diseases and comorbidities only if controlled co-expression of multiple AAV capsids is achieved on each transduced cell. We developed a tool to quantify the number of incoming AAV genomes that are co-expressed in the nervous system with single-cell resolution. By using an isogenic mix of three AAVs each expressing single fluorescent reporters, we determined that expression of much greater than 31 AAV genomes per neuron in vitro and 20 genomes per neuron in vivo is obtained across different brain regions including anterior cingulate, prefrontal, somatomotor and somatosensory cortex areas, and cerebellar lobule VI. Our results demonstrate that multiple AAV vectors containing different transgenes or transgene fragments, can efficiently co-express in the same neuron. This tool can be used to design and improve AAV-based interrogation of neuronal circuits, map brain connectivity, and treat genetic diseases affecting the nervous system

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand, a mixture of calcia, magnesia, alumina, and silicate, known as CMAS, is characterized by its high viscosity, density, and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics (mDPD) simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a coarse parametric ordinary differential equation (ODE) that captures the spreading radius behavior of the CMAS droplets. The ODE parameters are then identified based on the Physics-Informed Neural Network (PINN) framework. Subsequently, the closed form dependency of parameter values found by PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modeling and state-of-the-art machine learning techniques

MAVE-NN: learning genotype-phenotype maps from multiplex assays of variant effect

Multiplex assays of variant effect (MAVEs) are a family of methods that includes deep mutational scanning experiments on proteins and massively parallel reporter assays on gene regulatory sequences. Despite their increasing popularity, a general strategy for inferring quantitative models of genotype-phenotype maps from MAVE data is lacking. Here we introduce MAVE-NN, a neural-network-based Python package that implements a broadly applicable information-theoretic framework for learning genotype-phenotype maps-including biophysically interpretable models-from MAVE datasets. We demonstrate MAVE-NN in multiple biological contexts, and highlight the ability of our approach to deconvolve mutational effects from otherwise confounding experimental nonlinearities and noise

On the parameter combinations that matter and on those that do not: Data-driven studies of parameter (non)identifiability

We present a data-driven approach to characterizing nonidentifiability of a model’s parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically