Related papers: Data-driven discovery of self-similarity using neu…
In this work, we introduce a neural network algorithm designed to automatically identify similarity relations from data. By uncovering these similarity relations, our network approximates the underlying physical laws that relate…
Multiscale modeling of complex systems is crucial for understanding their intricacies. Data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. On the other hand,…
Thousands of person-years have been invested in searches for New Physics (NP), the majority of them motivated by theoretical considerations. Yet, no evidence of beyond the Standard Model (BSM) physics has been found. This suggests that…
Symmetries are key properties of physical models and of experimental designs, but any proposed symmetry may or may not be realized in nature. In this paper, we introduce a practical and general method to test such suspected symmetries in…
Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…
Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…
We show a data-driven approach to discover the underlying structural form of the mathematical equation governing the dynamics of multiple but similar systems induced by the same mechanisms. This approach hinges on theories that we lay out…
A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly.…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…
Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…
In control design most control strategies are model-based and require accurate models to be applied successfully. Due to simplifications and the model-reality-gap physics-derived models frequently exhibit deviations from real-world-systems.…
Multimodal problems are omnipresent in the real world: autonomous driving, robotic grasping, scene understanding, etc... We draw from the well-developed analysis of similarity to provide an example of a problem where neural networks are…
Estimating the parameters of a model describing a set of observations using a neural network is in general solved in a supervised way. In cases when we do not have access to the model's true parameters this approach can not be applied.…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…
Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data…
We present an approach for using machine learning to automatically discover the governing equations and hidden properties of real physical systems from observations. We train a "graph neural network" to simulate the dynamics of our solar…