Related papers: Informed Equation Learning

Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel…

The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…

Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Many analyses in particle and nuclear physics use simulations to infer fundamental, effective, or phenomenological parameters of the underlying physics models. When the inference is performed with unfolded cross sections, the observables…

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in…

Empirical data, on which deep learning relies, has substantial internal structure, yet prevailing theories often disregard this aspect. Recent research has led to the definition of structured data ensembles, aimed at equipping established…

When faced with learning challenging new tasks, humans often follow sequences of steps that allow them to incrementally build up the necessary skills for performing these new tasks. However, in machine learning, models are most often…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…

Despite tremendous progress over the past decade, deep learning methods generally fall short of human-level systematic generalization. It has been argued that explicitly capturing the underlying structure of data should allow connectionist…

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…

Most efforts in interpretability in deep learning have focused on (1) extracting explanations of a specific downstream task in relation to the input features and (2) imposing constraints on the model, often at the expense of predictive…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Structured prediction models aim at solving a type of problem where the output is a complex structure, rather than a single variable. Performing knowledge distillation for such models is not trivial due to their exponentially large output…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

We introduce an information-theoretic framework that views learning as universal prediction under log loss, characterized through regret bounds. Central to the framework is an effective notion of architecture-based model complexity, defined…

By integrating domain knowledge with labeled samples, informed machine learning has been emerging to improve the learning performance for a wide range of applications. Nonetheless, rigorous understanding of the role of injected domain…