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Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
We introduce Devito, a new domain-specific language for implementing high-performance finite difference partial differential equation solvers. The motivating application is exploration seismology where methods such as Full-Waveform…
This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
Graphs are widely used for representing pairwise interactions in complex systems. Since such real-world graphs are large and often evergrowing, sampling a small representative subgraph is indispensable for various purposes: simulation,…
Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system…
Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…
Embedded deformation nodes based formulation has been widely applied in deformable geometry and graphical problems. Though being promising in stereo (or RGBD) sensor based SLAM applications, it remains challenging to keep constant speed in…
We investigate the task of retrieving information from compositional distributed representations formed by Hyperdimensional Computing/Vector Symbolic Architectures and present novel techniques which achieve new information rate bounds.…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…