Related papers: Complexity Theory meets Ordinary Differential Equa…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
Based on our \bl{\textbf{Random Duality Theory (RDT)}}, in a sequence of our recent papers \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19}, we introduced a powerful algorithmic mechanism (called \bl{\textbf{CLuP}}) that can be…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
Microstructure evolution in matter is often modeled numerically using field or level-set solvers, mirroring the dual representation of spatiotemporal complexity in terms of pixel or voxel data, and geometrical forms in vector graphics.…
Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in…
The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…
This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We…
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing…
We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
Inspired by pioneering work of Ky\^uya Masuda in the 1980s, only much more recent PDE studies address global boundedness versus finite-time blow-up in complex time. The two phenomena are related by passage from real to purely imaginary…
We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
Time correlated fluctuations interacting with a spatial asymmetry potential are sufficient conditions to give rise to transport of Brownian particles. The transfer of information coming from the nonequilibrium bath, viewed as a source of…
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining dynamical systems machinery…
Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…