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Inspired by recent theoretical arguments, physics-informed echo state network (ESN) is discussed on the attempt to train a reservoir model absolutely in physics-informed manner. As the plainest work on such a purpose, an ODE (ordinary…
It is found that the coupled piNNN-NNN system breaks into fragments in a nontrivial way. Assuming the particles as distinguishable, there are indeed four modes of fragmentation into two clusters, while in the standard three-body problem…
In the recent years, Physics Informed Neural Networks (PINNs) have received strong interest as a method to solve PDE driven systems, in particular for data assimilation purpose. This method is still in its infancy, with many shortcomings…
Dynamical screening is a key property of charged many-particle systems. Its theoretical description is based on the $GW$ approximation that is extensively applied for ground-state and equilibrium situations but also for systems driven out…
We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
We compare the continuous and discrete truncated Wigner approximations of various spin models' dynamics to exact analytical and numerical solutions. We account for all components of spin-spin correlations on equal footing, facilitated by a…
We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
Distributed renewable generation, elastic loads, and purposeful manipulation of meter readings challenge the monitoring and control of today's power systems (PS). In this context, to maintain a comprehensive view of the system in real time,…
In this paper, a compact third-order gas-kinetic scheme is proposed for the compressible Euler and Navier-Stokes equations. The main reason for the feasibility to develop such a high-order scheme with compact stencil, which involves only…
Power flow (PF) calculations are fundamental to power system analysis to ensure stable and reliable grid operation. The Newton-Raphson (NR) method is commonly used for PF analysis due to its rapid convergence when initialized properly.…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation…
Physics-inspired graph neural networks (PI-GNNs) have been utilized as an efficient unsupervised framework for relaxing combinatorial optimization problems encoded through a specific graph structure and loss, reflecting dependencies between…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoretical model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of…
Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme…
Dynamic models of mechatronic systems are abundantly used in the context of motion control and design of complex servo applications. In practice, these systems are often plagued by unknown interactions, which make the physics-based…
Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ…