In recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of partial differential equations is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into convolutional neural networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. We demonstrate results on three-dimensional fully developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.

We present an approach to modeling the ground-state mass of atomic nuclei based directly on a probabilistic neural network constrained by relevant physics. Our physically interpretable machine learning (PIML) approach incorporates knowledge of physics by using a physically motivated feature space in addition to a soft physics constraint that is implemented as a penalty to the loss function. We train our PIML model on a random set of approximately 20% of the atomic mass evaluation (AME) and predict the remaining 80%. The success of our methodology is exhibited by a ${\sigma }_{\mathrm{rms}}\approx 186$ keV match to data for the training set and ${\sigma }_{\mathrm{rms}}\approx 316$ keV for the entire AME with $Z\ge 20$. We show that our general methodology can be interpreted using feature importance.

Direct Numerical Simulations (DNSs) of high Reynolds number turbulent flows, encountered in engineering, earth sciences, and astrophysics, are not tractable because of the curse of dimensionality associated with the number of degrees of freedom required to resolve all the dynamically significant spatio-temporal scales. Designing efficient and accurate Machine Learning (ML)-based reduced models of fluid turbulence has emerged recently as a promising approach to overcoming the curse of dimensionality challenge. However, to make the ML approaches reliable one needs to test their efficiency and accuracy, which is recognised as important but so far incomplete task. Aiming to improve this missing component of the promising approach, we design and evaluate two reduced models of 3D homogeneous isotropic turbulence and scalar turbulence based on state-of-the-art ML algorithms of the Deep Learning (DL) type: Convolutional Generative Adversarial Network (C-GAN) and Compressed Convolutional Long-Short-Term-Memory (CC-LSTM) Network. Quality and computational efficiency of the emulated velocity and scalar distributions is juxtaposed to the ground-truth DNS via physics-rich statistical tests. The reported results allow to uncover and classify weak and strong aspects of C-GAN and CC-LSTM. The reported results, as well as the physics-informed methodology developed to test the ML-based solutions, are expected to play a significant role in the future for making the DL schemes trustworthy through injecting and controlling missing physical information in computationally tractable ways.

OBJECTIVE: Intrathecal baclofen pumps are generally placed in children for the treatment of spasticity and dystonia. Use of implants in this pediatric population with comorbidities is reported to have a high risk of complications and infections. With the aim of reducing baclofen pump–related infections, a quality improvement project was instituted at the authors’ institution.METHODS: A workflow paradigm unique to baclofen pump implantation aimed at decreasing implant-related infections was implemented. All baclofen pump operations performed at the authors’ institution between August 2012 and June 2016 were reviewed. An infection prevention protocol was created and implemented in August 2014 based on a literature review and the consensus opinion of the pediatric neurosurgeons in the group. Compliance with the prevention bundle was tracked. Case outcomes before and after implementation of the protocol with a minimum of 3 months of follow-up were retrospectively reviewed. Univariate and multivariate analyses were performed to assess the association of the steps in the prevention bundle with infection and complication outcomes.RESULTS: A total of 128 baclofen pump surgeries were performed (64 preprotocol and 64 postprotocol). The patient age range was 3 to 27 years. The overall compliance rate with the infection prevention bundle was 82%. The pre- and postimplementation infection rates were 12.5% and 6.3%, respectively (p = 0.225). The total pre- and postimplementation complication rates were 23.4% and 9.4%, respectively (p = 0.032). The absolute and relative risk reductions for infections were 6.3% (95% CI 3.8%–16.3%) and 50%, respectively; for complications, the absolute and relative risk reductions were 14.1% (95% CI 1.5%–26.7%) and 60%, respectively.CONCLUSIONS: The total complication rate following intrathecal baclofen pump surgery was significantly lower after implementation of the quality improvement protocol. This study is an example of using checklist standardization to diminish special cause variability.

Reduced Order Modeling (ROM) for engineering applications has been a major research focus in the past few decades due to the unprecedented physical insight into turbulence offered by high-fidelity CFD. The primary goal of a ROM is to model the key physics/features of a flow-field without computing the full Navier-Stokes (NS) equations. This is accomplished by projecting the high-dimensional dynamics to a low-dimensional subspace, typically utilizing dimensionality reduction techniques like Proper Orthogonal Decomposition (POD), coupled with Galerkin projection. In this work, we demonstrate a deep learning based approach to build a ROM using the POD basis of canonical DNS datasets, for turbulent flow control applications. We find that a type of Recurrent Neural Network, the Long Short Term Memory (LSTM) which has been primarily utilized for problems like speech modeling and language translation, shows attractive potential in modeling temporal dynamics of turbulence. Additionally, we introduce the Hurst Exponent as a tool to study LSTM behavior for non-stationary data, and uncover useful characteristics that may aid ROM development for a variety of applications.