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The goals of this paper are two-fold. The first goal is to serve as an expository tutorial on the working of deep learning models which emphasizes geometrical intuition about the reasons for success of deep learning. The second goal is to…
** This article is published (open-access). ** A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations…
Symbolic Regression aims to automatically identify compact and interpretable mathematical expressions that model the functional relationship between input and output variables. Most existing search-based symbolic regression methods…
Neural networks have greatly boosted performance in computer vision by learning powerful representations of input data. The drawback of end-to-end training for maximal overall performance are black-box models whose hidden representations…
The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then…
Symbolic regression corresponds to an ensemble of techniques that allow to uncover an analytical equation from data. Through a closed form formula, these techniques provide great advantages such as potential scientific discovery of new…
Machine learning techniques have been applied to enhance turbulence modeling in recent years. However, the "black box" nature of most machine learning techniques poses significant interpretability challenges in improving turbulence models.…
Despite successful seminal works on passive systems in the literature, learning free-form physical laws for controlled dynamical systems given experimental data is still an open problem. For decades, symbolic mathematical equations and…
Data-driven surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an…
Symbolic regression has recently gained traction in AI-driven scientific discovery, aiming to recover explicit closed-form expressions from data that reveal underlying physical laws. Despite recent advances, existing methods remain…
Understanding the internal representations and decision mechanisms of deep neural networks remains a critical open challenge. While existing interpretability methods often identify influential input regions, they may not elucidate how a…
Deep learning provides a promising way to extract effective representations from raw data in an end-to-end fashion and has proven its effectiveness in various domains such as computer vision, natural language processing, etc. However, in…
Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However,…
We present a novel method for reliably explaining the predictions of neural networks. We consider an explanation reliable if it identifies input features relevant to the model output by considering the input and the neighboring data points.…
Neuro-encoded expression programming(NEEP) that aims to offer a novel continuous representation of combinatorial encoding for genetic programming methods is proposed in this paper. Genetic programming with linear representation uses…
While neural networks have been successfully applied to many natural language processing tasks, they come at the cost of interpretability. In this paper, we propose a general methodology to analyze and interpret decisions from a neural…
Interpretable mathematical expressions defining discrete-time dynamical systems (iterated maps) can model many phenomena of scientific interest, enabling a deeper understanding of system behaviors. Since formulating governing expressions…
Data-driven science and computation have advanced immensely to construct complex functional relationships using trainable parameters. However, efficiently discovering interpretable and accurate closed-form expressions from complex dataset…
Symbolic Regression (SR) is a type of regression analysis to automatically find the mathematical expression that best fits the data. Currently, SR still basically relies on various searching strategies so that a sample-specific model is…
Studying complex real-world phenomena often involves data from multiple views (e.g. sensor modalities or brain regions), each capturing different aspects of the underlying system. Within neuroscience, there is growing interest in…