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Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as…
We propose and apply simple machine learning approaches for recognition and classification of complex non-collinear magnetic structures in two-dimensional materials. The first approach is based on the implementation of the…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
In this paper, we advocate a novel spline-based isogeometric approach for boundary elements and its efficient implementation. We compare solutions obtained by both an isogeometric approach, and a classical parametric higher-order approach…
This survey is on recent advancements in the intersection of physical modeling and machine learning. We focus on the modeling of nonlinear systems which are closer to electric motors. Survey on motor control and fault detection in operation…
Representation learning has become an effective technique utilized by electronic design automation (EDA) algorithms, which leverage the natural representation of workflow elements as images, grids, and graphs. By addressing challenges…
The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects.…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
We demonstrate the use of model order reduction and neural networks for estimating the hysteresis properties of nanocrystalline permanent magnets from microstructure. With a data-driven approach, we learn the demagnetization curve from…
Numerical modeling of different structural materials that have highly nonlinear behaviors has always been a challenging problem in engineering disciplines. Experimental data is commonly used to characterize this behavior. This study aims to…
Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…
The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…
An unconventional magnet may be mapped onto a simple ferromagnet by the existence of a high-symmetry point. Knowledge of conventional ferromagnetic systems may then be carried over to provide insight into more complex orders. Here we…
Surrogate modelling is widely applied in computational science and engineering to mitigate computational efficiency issues for the real-time simulations of complex and large-scale computational models or for many-query scenarios, such as…
We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…