Related papers: GPLaSDI: Gaussian Process-based Interpretable Late…
Traditional partial differential equation (PDE) solvers can be computationally expensive, which motivates the development of faster methods, such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning and Bayesian ROM.…
Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has…
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…
Accurately solving partial differential equations (PDEs) is essential across many scientific disciplines. However, high-fidelity solvers can be computationally prohibitive, motivating the development of reduced-order models (ROMs).…
A parametric adaptive greedy Latent Space Dynamics Identification (gLaSDI) framework is developed for accurate, efficient, and certified data-driven physics-informed greedy auto-encoder simulators of high-dimensional nonlinear dynamical…
Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI)…
Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications.…
We propose an efficient thermodynamics-informed latent space dynamics identification (tLaSDI) framework for the reduced-order modeling of parametric nonlinear dynamical systems. This framework integrates autoencoders for dimensionality…
The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle…
Numerical solving parameterised partial differential equations (P-PDEs) is highly practical yet computationally expensive, driving the development of reduced-order models (ROMs). Recently, methods that combine latent space identification…
Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and…
We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The…
Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the…
This paper presents a machine learning framework (GP-NODE) for Bayesian systems identification from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in…
Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a…
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…
Directed energy deposition (DED) is a promising metal additive manufacturing technology capable of 3D printing metal parts with complex geometries at lower cost compared to traditional manufacturing. The technology is most effective when…
Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of…
Non-local thermodynamic equilibrium (NLTE) calculations remain a major computational bottleneck in radiation--hydrodynamics, while most existing machine-learning surrogates treat NLTE as a static input--output mapping rather than a kinetic…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…