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In this work, we propose a disentangled latent optimization-based method for parameterizing grouped deforming 3D objects into shape and deformation factors in an unsupervised manner. Our approach involves the joint optimization of a…

We propose a natural solution to the cosmological constant problem consistent with the standard cosmology and successful over a broad range of energies. This solution is based on the existence of a new field, the devaluton, with its…

Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations…

We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Value decomposition has long been a fundamental technique in multi-agent dynamic programming and reinforcement learning (RL). Specifically, the value function of a global state $(s_1,s_2,\ldots,s_N)$ is often approximated as the sum of…

Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and…

Kinetic models of solid thermal decomposition are traditionally used for individual fit of isothermal decomposition experimental data. However, this methodology can provide unacceptable errors in some cases. To solve this problem, a neural…

Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…

The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Near-term prediction of the structured spatio-temporal processes driving our climate is of profound importance to the safety and well-being of millions, but the prounced nonlinear convection of these processes make a complete mechanistic…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…

Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…

Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional…

Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…