Related papers: Finite Information Numbers through the Inductive C…
Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the…
In this paper, we develop a framework for information theoretic learning based on infinitely divisible matrices. We formulate an entropy-like functional on positive definite matrices based on Renyi's axiomatic definition of entropy and…
PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…
In this thesis, we develop algorithms similar to the Gaussian elimination algorithm in symplectic and split orthogonal similitude groups. As an application to this algorithm, we compute the spinor norm for split orthogonal groups. Also, we…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are a fundamental model in inventory management, manufacturing, and logistics that capture these…
We consider a fractional-calculus example of a continuous hierarchy of algorithmic information in the context of its potential applications in digital twinning. Digital twinning refers to different emerging methodologies in control…
Compressing large data sets to a manageable number of summaries that are informative about the underlying parameters vastly simplifies both frequentist and Bayesian inference. When only simulations are available, these summaries are…
Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…
We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the…
We extend the finite element interpolated neural network (FEINN) framework from partial differential equations (PDEs) with weak solutions in $H^1$ to PDEs with weak solutions in $H(\textbf{curl})$ or $H(\textbf{div})$. To this end, we…
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…
We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…
Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \emph{pinning subspaces}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a \emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the constraint…
Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…
The work is devoted to study of the following problem: can we use any qualitative criteria for realization of such universal phenomenon as self-organization in open systems? We have defined values of information at fixed points of…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…