Related papers: Guessing With Quadratic Differential Equations

By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…

We motivate the use of differentiable probabilistic programming techniques in order to account for the large model-space inherent to astrophysical $\gamma$-ray analyses. Targeting the longstanding Galactic Center $\gamma$-ray Excess (GCE)…

We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…

The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…

We present a software package that guesses formulae for sequences of, for example, rational numbers or rational functions, given the first few terms. We implement an algorithm due to Bernhard Beckermann and George Labahn, together with some…

We provide a learning-based technique for guessing a winning strategy in a parity game originating from an LTL synthesis problem. A cheaply obtained guess can be useful in several applications. Not only can the guessed strategy be applied…

This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…

The gap probability generating function has as its coefficients the probability of an interval containing exactly $k$ eigenvalues. For scaled random matrices with orthogonal symmetry, and the interval at the hard or soft spectrum edge, the…

Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…

Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…

Generative deep learning methods built upon Convolutional Neural Networks (CNNs) provide a great tool for predicting non-linear structure in cosmology. In this work we predict high resolution dark matter halos from large scale, low…

The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes…

Equation discovery, also known as symbolic regression, is a type of automated modeling that discovers scientific laws, expressed in the form of equations, from observed data and expert knowledge. Deterministic grammars, such as context-free…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

Deep clustering as an important branch of unsupervised representation learning focuses on embedding semantically similar samples into the identical feature space. This core demand inspires the exploration of contrastive learning and…

Score-based models have recently been introduced as a richer framework to model distributions in high dimensions and are generally more suitable for generative tasks. In score-based models, a generative task is formulated using a parametric…

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been…

Stochastic processes are often represented through orthonormal series expansions, a framework originating in the classical works of Lo\`eve and Karhunen and widely used for simulation and numerical approximation. While truncation error in…

Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…