Related papers: A random rule model of surface growth
Stochastic neural networks (SNNs) are random functions whose predictions are gained by averaging over multiple realizations. Consequently, a gradient-based adversarial example is calculated based on one set of samples and its classification…
One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However,…
In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction.…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical…
Bayesian Additive Regression Trees [BART, Chipman et al., 2010] have gained significant popularity due to their remarkable predictive performance and ability to quantify uncertainty. However, standard decision tree models rely on recursive…
Surfaces sputtered by ion beam bombardment have been known to exhibit patterns whose behavior is modeled with stochastic partial differential equations. However, we apply a new approach by the use of the famous Lorentz equations to simulate…
We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization…
Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and…
Many real phenomena may be modelled as locally finite unions of $d$-dimensional time dependent random closed sets in $\mathbb{R}^d$, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as…
Computer modelling for evolutionary systems consists in: 1) to store in the memory the individual features of each member of a large population; and 2) to update the whole system repeatedly, as time goes by, according to some prescribed…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
This paper introduces a new approach for continual planning and model learning in relational, non-stationary stochastic environments. Such capabilities are essential for the deployment of sequential decision-making systems in the uncertain…
In biology and ecology, individuals or communities of individuals living in unpredictable environments often alternate between different evolutionary strategies to spread and reduce risks. Such behavior is commonly referred to as…
Motivated by a series of experiments that revealed a temperature dependence of the dynamic scaling regime of growing surfaces, we investigate theoretically how a nonequilibrium growth process reacts to a sudden change of system parameters.…
Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and…
Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…