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The act of measurement on a quantum state is supposed to "collapse" the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function,…
It is shown that the classical book by von Neumann proposing dynamics of measured systems with "reduction (or collapse) of system's wave packet" contains also hints how to avoid this discontinuity in time evolution of the measured system…
This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…
Over the last half-century, linear viscoelastic models for crack growth in soft solids have flourished but their predictions have rarely been compared to experiments. In fact, most available models are either very approximate or cast in…
Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…
Continuous machine learning pipelines are common in industrial settings where models are periodically trained on data streams. Unfortunately, concept drifts may occur in data streams where the joint distribution of the data X and label y,…
We show that long standing debates on the collapse and the role of the observer in quantum mechanics can be resolved experimentally via a nondistructive continuous monitoring of a single quantum system. An example of such a system, coupled…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
Quantifying the similarity of two or more datasets has widespread applications in statistics and machine learning. The method choice is, however, difficult due to the abundance of proposed methods and the lack of neutral comparison studies,…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
The training dynamics of deep neural networks often defy expectations, even as these models form the foundation of modern machine learning. Two prominent examples are grokking, where test performance improves abruptly long after the…
We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical fatigue.…
Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of…
Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…
Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack…
The advent of modern technology, permitting the measurement of thousands of characteristics simultaneously, has given rise to floods of data characterized by many large or even huge datasets. This new paradigm presents extraordinary…
Synthetic data describing coherent random fluctuations have widely been used to validate numerical sim- ulations against experimental observations or to examine the reliability of extracting statistical properties of plasma turbulence via…
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…