Pouria Mistani

NVIDIA | Nvidia

We present a scalable strategy for development of mesh-free hybrid neuro-symbolic partial differential equation solvers based on existing mesh-based numerical discretization methods. Particularly, this strategy can be used to efficiently train neural network surrogate models for the solution functions and operators of partial differential equations...

We present a highly scalable strategy for developing mesh-free neuro-symbolic partial differential equation solvers from existing numerical discretizations found in scientific computing. This strategy is unique in that it can be used to efficiently train neural network surrogate models for the solution functions and the differential operators, whil...

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the accuracy and reliability of existing numerical algorithms for partial differential equations as custom layers i...

We present a theoretical framework to model the electric response of cell aggregates. We establish a coarse representation for each cell as a combination of membrane and cytoplasm dipole moments. Then we compute the effective conductivity of the resulting system, and thereafter derive a Fokker-Planck partial differential equation that captures the...

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the accuracy and reliability of existing numerical algorithms for partial differential equations as custom layers i...

Complex networks are composed of nodes (entities) and edges (connections) with any arbitrary topology. There may also exist multiple types of interactions among these nodes and each node may admit different states in each of its interactions with its neighbors. Understanding complex networks dwells on understanding their structure and function. How...

In this chapter, following the previous one, we briefly present the modern approach to real-space renormalization group (RG) theory based on tensor network formulations which was developed during the last two decades. The aim of this sequel is to suggest a novel framework based on tensor networks in order to find the fixed points of complex systems...

Complex networks are composed of nodes (entities) and edges (connections) with any arbitrary topology. There may also exist multiple types of interactions among these nodes and each node may admit different states in each of its interactions with its neighbors. Understanding complex networks dwells on understanding their structure and function. How...

Electropermeabilization (also called electroporation) is a significant increase in the electrical conductivity and permeability of the cell membrane that occurs when pulses of large amplitude (a few hundred volts per centimeter) are applied to the cells. • Due to the electric field, the cell membrane is permeabilized, and then non-permeant molecule...

We introduce a numerical framework that enables unprecedented direct numerical studies of the electropermeabilization effects of a cell aggregate at the meso-scale. Our simulations qualitatively replicate the shadowing effect observed in experiments and reproduce the time evolution of the impedance of the cell sample in agreement with the trends ob...

We introduce an approach for simulating epitaxial growth by use of an island dynamics model on a forest of quadtree grids, and in a parallel environment. To this end, we use a parallel framework introduced in the context of the level-set method. This framework utilizes: discretizations that achieve a second-order accurate level-set method on non-gr...

Galaxy clusters contain a large population of low mass dwarf elliptical galaxies whose exact origin is unclear: their colors, structural properties and kinematics differ substantially from those of dwarf irregulars in the field. We use the Illustris cosmological simulation to study differences in the assembly paths of dwarf galaxies (3e8 < M_*/M_su...

Dwarf spheroidal galaxies are representing the largest mass dis- crepancies in the local universe. Apart from that, “Cetus” a dSph discovered by Whiting et al. (1999) which is also the farthest known dwarf spheroidal galaxy residing on the boundaries of the local group of galaxies is of increased interest, not only because it can constrain the tota...