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In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete…
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are…
Automatic software generation based on some specification is known as program synthesis. Most existing approaches formulate program synthesis as a search problem with discrete parameters. In this paper, we present a novel formulation of…
Evolutionary Computation is a group of biologically inspired algorithms used to solve complex optimisation problems. It can be split into Evolutionary Algorithms, which take inspiration from genetic inheritance, and Swarm Intelligence…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
The synthesis of product design concepts stands at the crux of early-phase development processes for technical products, traditionally posing an intricate interdisciplinary challenge. The application of deep learning methods, particularly…
Evolutionary algorithms have been used in the digital art scene since the 1970s. A popular application of genetic algorithms is to optimize the procedural placement of vector graphic primitives to resemble a given painting. In recent years,…
Multi Expression Programming (MEP) is a Genetic Programming variant which encodes multiple solutions in a single chromosome. This paper introduces and deeply describes several strategies for solving binary and multi-class classification…
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…
The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…
Given the recent impressive accomplishments of language models (LMs) for code generation, we explore the use of LMs as adaptive mutation and crossover operators for an evolutionary neural architecture search (NAS) algorithm. While NAS still…
The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…
In model-driven engineering, developing a textual domain-specific language (DSL) involves constructing a meta-model, which defines an underlying abstract syntax, and a grammar, which defines the concrete syntax for the DSL. Language…
Program synthesis aims to {\it automatically} find programs from an underlying programming language that satisfy a given specification. While this has the potential to revolutionize computing, how to search over the vast space of programs…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
Automated algorithm discovery in scientific computing faces fundamental challenges: vast design spaces with expensive evaluations, domain-specific physical constraints requiring expert knowledge, and the necessity for interpretable…