Related papers: PROSE: Predicting Operators and Symbolic Expressio…

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

Symbolic regression is essential for deriving interpretable expressions that elucidate complex phenomena by exposing the underlying mathematical and physical relationships in data. In this paper, we present an advanced symbolic regression…

The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…

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…

The goal of neuro-symbolic AI is to integrate symbolic and subsymbolic AI approaches, to overcome the limitations of either. Prominent systems include Logic Tensor Networks (LTN) or DeepProbLog, which offer neural predicates and end-to-end…

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…

Existing machine learning methods for molecular (e.g., gene) embeddings are restricted to specific tasks or data modalities, limiting their effectiveness within narrow domains. As a result, they fail to capture the full breadth of gene…

Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…

Neural networks have the ability to serve as universal function approximators, but they are not interpretable and don't generalize well outside of their training region. Both of these issues are problematic when trying to apply standard…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

How can neural networks perform so well on compositional tasks even though they lack explicit compositional representations? We use a novel analysis technique called ROLE to show that recurrent neural networks perform well on such tasks by…

Multimodal models integrating natural language and visual information have substantially improved generalization of representation models. However, their effectiveness significantly declines in real-world situations where certain modalities…

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential…

Multimodal stock trading volume movement prediction with stock-related news is one of the fundamental problems in the financial area. Existing multimodal works that train models from scratch face the problem of lacking universal knowledge…