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Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved…

Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…

Data-driven discovery of governing equations is of great significance for helping us understand intrinsic mechanisms and build physical models. Recently, numerous highly innovative algorithms have emerged, aimed at inversely discovering the…

We analyse the search behaviour of genetic programming for symbolic regression in practically relevant but limited settings, allowing exhaustive enumeration of all solutions. This enables us to quantify the success probability of finding…

Genetic programming (GP) is the state-of-the-art in financial automated feature construction task. It employs reverse polish expression to represent features and then conducts the evolution process. However, with the development of deep…

Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements of model identification from adequate data, how to unravel the models from limited data is less…

The advent of Large Language Models (LLMs) has opened new frontiers in automated algorithm design, giving rise to numerous powerful methods. However, these approaches retain critical limitations: they require extensive evaluation of the…

In recent years, symbolic regression has been of wide interest to provide an interpretable symbolic representation of potentially large data relationships. Initially circled to genetic algorithms, symbolic regression methods now include a…

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation…

In recent years, genetic programming (GP)-based evolutionary feature construction has achieved significant success. However, a primary challenge with evolutionary feature construction is its tendency to overfit the training data, resulting…

Compact symbolic expressions have been shown to be more efficient than neural network models in terms of resource consumption and inference speed when implemented on custom hardware such as FPGAs, while maintaining comparable…

Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…

Current biocomputing approaches predominantly rely on engineered circuits with fixed logic, offering limited stability and reliability under diverse environmental conditions. Here, we use the GRNN framework introduced in our previous work…

Algorithmic discovery has traditionally relied on human ingenuity and extensive experimentation. Here we investigate whether a prominent scientific computing algorithm, the Kalman Filter, can be discovered through an automated, data-driven,…

Interpretability and uncertainty quantification in machine learning can provide justification for decisions, promote scientific discovery and lead to a better understanding of model behavior. Symbolic regression provides inherently…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

Among the evolutionary methods, one that is quite prominent is Genetic Programming, and, in recent years, a variant called Geometric Semantic Genetic Programming (GSGP) has shown to be successfully applicable to many real-world problems.…

Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…