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This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
We investigate the type of the temperature phase transition in the $N$ component $\la \phi^4$ ($O(N)$) model of scalar fields. Actual calculations are carried out in the beyond-super-daisy approximation (BSDA). The cases $N = 1$ and larger…
Semi-supervised anomaly detection is a common problem, as often the datasets containing anomalies are partially labeled. We propose a canonical framework: Semi-supervised Pseudo-labeler Anomaly Detection with Ensembling (SPADE) that isn't…
The spin-diode effect is studied both experimentally and with our original semi-analytical method. The latter is based on an improved version of the Thiele equation approach (TEA) that we combine to micromagnetic simulation data to…
We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
We apply variational principles from statistical physics and the Landau theory of phase transitions to multicomponent alloys using the multiple-scattering theory of Korringa-Kohn-Rostoker (KKR) and the coherent potential approximation…
We propose a systematic methodology to identify the topological phase transition through a self-supervised machine learning model, which is trained to correlate system parameters to the non-local observables in time-of-flight experiments of…
Stacking fault energy (SFE) is of the most critical microstructure attribute for controlling the deformation mechanism and optimizing mechanical properties of austenitic steels, while there are no accurate and straightforward computational…
For an empirical signed measure $\mu = \frac{1}{N} \left(\sum_{i=1}^P \delta_{x_i} - \sum_{i=1}^M \delta_{y_i}\right)$, particle annihilation (PA) removes $N_A$ particles from both $\{x_i\}_{i=1}^P$ and $\{y_i\}_{i=1}^M$ simultaneously,…
Model identification is a crucial problem in chemical industries. In recent years, there has been increasing interest in learning data-driven models utilizing partial knowledge about the system of interest. Most techniques for model…
We demonstrate the utility of an unsupervised machine learning tool for the detection of phase transitions in off-lattice systems. We focus on the application of principal component analysis (PCA) to detect the freezing transitions of…
Discharge of hazardous substances into the marine environment poses a substantial risk to both public health and the ecosystem. In such incidents, it is imperative to accurately estimate the release strength of the source and reconstruct…
Autonomous Experimentation Platforms (AEPs) are advanced manufacturing platforms that, under intelligent control, can sequentially search the material design space (MDS) and identify parameters with the desired properties. At the heart of…
This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical…
Understanding how cellular morphology, gene expression, and spatial context jointly shape tissue function is a central challenge in biology. Image-based spatial transcriptomics technologies now provide high-resolution measurements of cell…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…