Related papers: Rediscovering Hyperelasticity by Deep Symbolic Reg…
A great variety of models can describe the non-linear response of rubber to uni-axial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three…
Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
Process-structure-property relationships are fundamental in materials science and engineering and are key to the development of new and improved materials. Symbolic regression serves as a powerful tool for uncovering mathematical models…
This work presents a hyper-viscoelastic model based on the Hencky-logarithmic strain tensor to model the response of a Tire Derived Material (TDM) undergoing moderately large deformations. TDM is a composite made by cold forging a mix of…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…
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…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
As an integral part of contemporary manufacturing, monitoring systems obtain valuable information during machining to oversee the condition of both the process and the machine. Recently, diverse algorithms have been employed to detect tool…
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and…
This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize…
A Deep Learning approach is devised to estimate the elastic energy density $\rho$ at the free surface of an undulated stressed film. About 190000 arbitrary surface profiles h(x) are randomly generated by Perlin noise and paired with the…
As power systems evolve with the increasing integration of renewable energy sources and smart grid technologies, there is a growing demand for flexible and scalable modeling approaches capable of capturing the complex dynamics of modern…
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…
The deep energy method (DEM) has been used to solve the elastic deformation of structures with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on the principle of minimum potential energy. In this…
Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty…
We explore the use of symbolic regression to derive compact analytical expressions for angular observables relevant to electroweak boson production at the Large Hadron Collider (LHC). Focusing on the angular coefficients that govern the…