Sub-grid modelling for two-dimensional turbulence using neural networks

In this investigation, a data-driven turbulence closure framework is introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the sub-grid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a-priori and a-posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability density function based validation of sub-grid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for sub-grid quantity inference. In addition, it is also observed that some measure of a-posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data

Label-Free Intracellular Multi-Specificity in Yeast Cells by Phase-Contrast Tomographic Flow Cytometry

: In-flow phase-contrast tomography provides a 3D refractive index of label-free cells in cytometry systems. Its major limitation, as with any quantitative phase imaging approach, is the lack of specificity compared to fluorescence microscopy, thus restraining its huge potentialities in single-cell analysis and diagnostics. Remarkable results in introducing specificity are obtained through artificial intelligence (AI), but only for adherent cells. However, accessing the 3D fluorescence ground truth and obtaining accurate voxel-level co-registration of image pairs for AI training is not viable for high-throughput cytometry. The recent statistical inference approach is a significant step forward for label-free specificity but remains limited to cells' nuclei. Here, a generalized computational strategy based on a self-consistent statistical inference to achieve intracellular multi-specificity is shown. Various subcellular compartments (i.e., nuclei, cytoplasmic vacuoles, the peri-vacuolar membrane area, cytoplasm, vacuole-nucleus contact site) can be identified and characterized quantitatively at different phases of the cells life cycle by using yeast cells as a biological model. Moreover, for the first time, virtual reality is introduced for handling the information content of multi-specificity in single cells. Full fruition is proofed for exploring and interacting with 3D quantitative biophysical parameters of the identified compartments on demand, thus opening the route to a metaverse for 3D microscopy

The signal within the noise: efficient inference of stochastic gene regulation models using fluorescence histograms and stochastic simulations

Motivation: In the noisy cellular environment, stochastic fluctuations at the molecular level manifest as cell-cell variability at the population level that is quantifiable using high-throughput single-cell measurements. Such variability is rich with information about the cell's underlying gene regulatory networks, their architecture and the parameters of the biochemical reactions at their core. Results: We report a novel method, called Inference for Networks of Stochastic Interactions among Genes using High-Throughput data (INSIGHT), for systematically combining high-throughput time-course flow cytometry measurements with computer-generated stochastic simulations of candidate gene network models to infer the network's stochastic model and all its parameters. By exploiting the mathematical relationships between experimental and simulated population histograms, INSIGHT achieves scalability, efficiency and accuracy while entirely avoiding approximate stochastic methods. We demonstrate our method on a synthetic gene network in bacteria and show that a detailed mechanistic model of this network can be estimated with high accuracy and high efficiency. Our method is completely general and can be used to infer models of signal-activated gene networks in any organism based solely on flow cytometry data and stochastic simulations. Availability: A free C source code implementing the INSIGHT algorithm, together with test data is available from the authors. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Normalisation Control in Deep Inference via Atomic Flows

We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations. This allows us to prove, for propositional logic, a new and very general normalisation theorem, which contains cut elimination as a special case. We operate in deep inference, which is more general than other syntactic paradigms, and where normalisation is more difficult to control. We argue that atomic flows are a significant technical advance for normalisation theory, because 1) the technique they support is largely independent of syntax; 2) indeed, it is largely independent of logical inference rules; 3) they constitute a powerful geometric formalism, which is more intuitive than syntax

Spatial inference of traffic transition using micro-macro traffic variables

This paper proposes an online traffic inference algorithm for road segments in which local traffic information cannot be directly observed. Using macro-micro traffic variables as inputs, the algorithm consists of three main operations. First, it uses interarrival time (time headway) statistics from upstream and downstream locations to spatially infer traffic transitions at an unsupervised piece of segment. Second, it estimates lane-level flow and occupancy at the same unsupervised target site. Third, it estimates individual lane-level shockwave propagation times on the segment. Using real-world closed-circuit television data, it is shown that the proposed algorithm outperforms previously proposed methods in the literature

Mining gold from implicit models to improve likelihood-free inference

Simulators often provide the best description of real-world phenomena. However, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based inference techniques that go beyond the traditional Approximate Bayesian Computation approach, which struggles in a high-dimensional setting, and extend methods that use surrogate models based on neural networks. We show that additional information, such as the joint likelihood ratio and the joint score, can often be extracted from simulators and used to augment the training data for these surrogate models. Finally, we demonstrate that these new techniques are more sample efficient and provide higher-fidelity inference than traditional methods.Comment: Code available at https://github.com/johannbrehmer/simulator-mining-example . v2: Fixed typos. v3: Expanded discussion, added Lotka-Volterra example. v4: Improved clarit

On the relative proof complexity of deep inference via atomic flows

We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show that these systems, as well as bounded-depth Frege systems, cannot polynomially simulate KS, by giving polynomial-size proofs of certain variants of the propositional pigeonhole principle in KS.Comment: 27 pages, 2 figures, full version of conference pape