arXiv subjects

Junlin Li

Publications and source records attributed to Junlin Li.

59 records · Page 4Linked to original sources

arXiv2019

High-Dimensional Dynamic Systems Identification with Additional Constraints

This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of the data. To alleviate this problem, we first formulate this identification problem into a multivariate linear regression problem with row-sub-Gaussian measurement matrix using the more general input designs and the independent repeated sampling schemes. We then propose a nuclear norm heuristic method that estimates the parameter matrix of dynamic system from a few input-state data samples. Based on this, we can extend the existing results. In this paper, we consider two scenarios. (i) In the noiseless scenario, nuclear-norm minimization is introduced for promoting low-rank. We define the notion of weak restricted isometry property, which is weaker than the ordinary restricted isometry property, and show it holds with high probability for the row-sub-Gaussian measurement matrix. Thereby, the rank-minimization matrix can be exactly recovered from finite number of data samples. (ii) In the noisy scenario, a regularized framework involving nuclear norm penalty is established. We give the notion of operator norm curvature condition for the loss function, and show it holds for row-sub-Gaussian measurement matrix with high probability. Consequently, when specifying the suitable choice of the regularization parameter, the operator norm error of the optimal solution of this program has a sharp bound given a finite amount of data samples. This operator norm error bound is stronger than the ordinary Frobenius norm error bound obtained in the existing work.

math.ST↗

arXiv2019

Machine Discovery of Partial Differential Equations from Spatiotemporal Data

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which physical terms are necessary and which can be removed (because they are physically negligible in the sense that they do not affect the dynamics too much) from a pool of candidate functions. The method is built on the recent development of Sparse Bayesian Learning; which enforces the sparsity in the to-be-identified PDEs, and therefore can balance the model complexity and fitting error with theoretical guarantees. Without leveraging prior knowledge or assumptions in the discovery process, we use an automated approach to discover ten types of PDEs, including the famous Navier-Stokes and sine-Gordon equations, from simulation data alone. Moreover, we demonstrate our data-driven discovery process with the Complex Ginzburg-Landau Equation (CGLE) using data measured from a traveling-wave convection experiment. Our machine discovery approach presents solutions that has the potential to inspire, support and assist physicists for the establishment of physical laws from measured spatiotemporal data, especially in notorious fields that are often too complex to allow a straightforward establishment of physical law, such as biophysics, fluid dynamics, neuroscience or nonlinear optics.

stat.ML↗

arXiv2018

Quantum Random Number Generator based on Tunneling effects in Si Diode

Previously, we built up a set of photon-free quantum random number generator(QRNG) with InGaAs single photon avalanche diodes. We exploited the stochastic property of quantum tunneling effect. Here, we utilized tunneling signals in Si diodes to implement quantum random number generator. In our experiment, instead of applying periodic pulses between the diode as we did in the InGaAs QRNG, we applied fixed voltage and detect time intervals between adjacent tunneling signals, as random source. This Si QRNG has a high performance in the randomness of its raw data and almost post-processing-free. Final data rate in our experiment is 6.98MB/s and could reach 23MB/s if the temperature-control system is ameliorated.

quant-ph↗

arXiv2017

Quantum random number generator based on quantum tunneling effect

In this paper, we proposed an experimental implementation of quantum random number generator(QRNG) with inherent randomness of quantum tunneling effect of electrons. We exploited InGaAs/InP diodes, whose valance band and conduction band shared a quasi-constant energy barrier. We applied a bias voltage on the InGaAs/InP avalanche diode, which made the diode works under Geiger mode, and triggered the tunneling events with a periodic pulse. Finally, after data collection and post-processing, our quantum random number generation rate reached 8Mb/s, and final data was verified by NIST test and Diehard test. Our experiment is characterized as an innovative low-cost, photonic source free, integratable or even chip-achievable method in quantum random number generation.

quant-ph↗

arXiv2013

Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix

We study multipartite entanglement under stochastic local operations and classical communication (SLOCC) and propose the entanglement classification under SLOCC for arbitrary-dimensional multipartite ($n$-qudit) pure states via the rank of coefficient matrix, together with the permutation of qudits. The ranks of the coefficient matrices have been proved to be entanglement monotones. The entanglement classification of the $2 \otimes 2 \otimes 2 \otimes 4$ system is discussed in terms of the generalized method, and 22 different SLOCC families are found.

quant-ph↗