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Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We consider an evolutionary PDE system coupling the Cahn-Hilliard equation with singular potential, mass source and transport effects, to a Brinkman-type relation for the macroscopic velocity field and to a further equation describing the…
When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction, and…
We apply a temporal edge prediction model for weighted dynamic graphs to predict time-dependent changes in molecular structure. Each molecule is represented as a complete graph in which each atom is a vertex and all vertex pairs are…
Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of…
Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the…
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…
Chemotaxis is the physical phenomenon that bacteria adjust their motions according to chemical stimulus. A classical model for this phenomenon is a kinetic equation that describes the velocity jump process whose tumbling/transition kernel…
Cosmic-ray acceleration processes in astrophysical plasmas are often investigated with fully-kinetic or hybrid kinetic numerical simulations, which enable us to describe a detailed microphysics of particle energization mechanisms. Tracing…
While neural networks can be approximated by linear models as their width increases, certain properties of wide neural networks cannot be captured by linear models. In this work we show that recently proposed Neural Quadratic Models can…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible computational cost of such surrogates renders them an attractive…
Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…
Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…
Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective…
A slowly-varying or thin-layer multiscale assumption empowers macroscale understanding of many physical scenarios from dispersion in pipes and rivers, including beams, shells, and the modulation of nonlinear waves, to homogenisation of…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
Molecular property calculations are the bedrock of chemical physics. High-fidelity \textit{ab initio} modeling techniques for computing the molecular properties can be prohibitively expensive, and motivate the development of…