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We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover…

The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a…

In some situations, the interpretability of the machine learning models plays a role as important as the model accuracy. Interpretability comes from the need to trust the prediction model, verify some of its properties, or even enforce them…

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

Learning from complex real-life networks is a lively research area, with recent advances in learning information-rich, low-dimensional network node representations. However, state-of-the-art methods are not necessarily interpretable and are…

Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value…

Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…

Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…

Many machine learning strategies designed to automate mathematical tasks leverage neural networks to search large combinatorial spaces of mathematical symbols. In contrast to traditional evolutionary approaches, using a neural network at…

Complex networks describe important structures in nature and society, composed of nodes and the edges that connect them. The evolution of these networks is typically described by dynamics, which are labor-intensive and require expert…

Robots that interact with humans in a physical space or application need to think about the person's posture, which typically comes from visual sensors like cameras and infra-red. Artificial intelligence and machine learning algorithms use…

Symbolic regression (SR) methods attempt to learn mathematical expressions that approximate the behavior of an observed system. However, when dealing with multivariate systems, they often fail to identify the functional form that explains…

Inspired by long-standing open problems in algebraic combinatorics, we show that modern machine learning can meaningfully contribute to verifiable mathematical discoveries. In particular, we focus on the construction of simple mathematical…

Photoelastic techniques have a long tradition in both qualitative and quantitative analysis of the stresses in granular materials. Over the last two decades, computational methods for reconstructing forces between particles from their…

In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error…

Recent studies on Learning to Optimize (L2O) suggest a promising path to automating and accelerating the optimization procedure for complicated tasks. Existing L2O models parameterize optimization rules by neural networks, and learn those…

This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the…

Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…