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TensorFlow is a popular deep learning framework used by data scientists to solve a wide-range of machine learning and deep learning problems such as image classification and speech recognition. It also operates at a large scale and in…
In this paper, we explore how to leverage large language models (LLMs) to solve mathematical problems efficiently and accurately. Specifically, we demonstrate the effectiveness of classifying problems into distinct categories and employing…
We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi and Gauss-Seidel, or with Krylov methods, e.g., GMRES and…
Modeling multiphysics processes in porous media requires preconditioned iterative linear solvers to enable efficient simulations at industry-relevant scales. These solvers are typically composed of sub-algorithms that target individual…
The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…
Reasoning about 3D scenes from their 2D image projections is one of the core problems in computer vision. Solutions to this inverse and ill-posed problem typically involve a search for models that best explain observed image data. Notably,…
Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra…
Domain adaptation is a sub-field of machine learning that involves transferring knowledge from a source domain to perform the same task in the target domain. It is a typical challenge in machine learning that arises, e.g., when data is…
A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
Programs to solve so-called constraint problems are complex pieces of software which require many design decisions to be made more or less arbitrarily by the implementer. These decisions affect the performance of the finished solver…
Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this…
In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…
Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…
To acquire a new skill, humans learn better and faster if a tutor, based on their current knowledge level, informs them of how much attention they should pay to particular content or practice problems. Similarly, a machine learning model…
Dealing with planning problems with both logical relations and numeric changes in real-world dynamic environments is challenging. Existing numeric planning systems for the problem often discretize numeric variables or impose convex…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
The stabilization of time series processes is a crucial problem that is ubiquitous in various industrial fields. The application of machine learning to its solution can have a decisive impact, improving both the quality of the resulting…
For many machine learning algorithms, predictive performance is critically affected by the hyperparameter values used to train them. However, tuning these hyperparameters can come at a high computational cost, especially on larger datasets,…