Related papers: Pick-and-Mix Information Operators for Probabilist…
Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers which seem sufficiently accurate for the forward…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…
We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for…
This paper presents the first slicing approach for probabilistic programs based on specifications. We show that when probabilistic programs are accompanied by their specifications in the form of pre- and post-condition, we can exploit this…
A subroutine for very-high-precision numerical solution of a class of ordinary differential equations is provided. For given evaluation point and equation parameters the memory requirement scales linearly with precision $P$, and the number…
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…
Ising machines can solve combinatorial optimization problems by representing them as energy minimization problems. A common implementation is the probabilistic Ising machine (PIM), which uses probabilistic (p-) bits to represent coupled…
It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various…
The aim of this paper is twofold. First, we obtain the explicit exact formal solutions of differential equations of different types in the form with Dyson chronological operator exponents. This allows us to deal directly with the solutions…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
In this paper, we consider the initial value problem for some nonlinear second-order ODEs of Duffing type. We study the large time behavior of the solutions to this problem, from both the perspectives of mathematical and numerical analysis.…
With the growth of data and necessity for distributed optimization methods, solvers that work well on a single machine must be re-designed to leverage distributed computation. Recent work in this area has been limited by focusing heavily on…
Qualitative probabilistic reasoning in a Bayesian network often reveals tradeoffs: relationships that are ambiguous due to competing qualitative influences. We present two techniques that combine qualitative and numeric probabilistic…
Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background…
Real-world problems typically require the simultaneous optimization of several, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables…
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…