Experimental Analysis and Multiscale Modeling of the Dynamics of a Fiber-Optic Coil

Fiber-optic gyroscopes (FOGs) are common rotation measurement devices in aerospace applications. They have a wide range of diversity in length and in the winding radius of the coil to meet system requirements. Every dimensional parameter in the coil influences the dynamic response of the system, eventually leading to measurement errors. In order to eliminate the errors and to qualify the system, after the design and production stages, a deep and comprehensive testing procedure follows. In this study, the dynamic behavior of a quadrupole wound fiber-optic coil is investigated. First, pre-wound fiber-optic coils are tested with an impact modal test, where the mode shapes and natural frequencies are determined with structural data acquisition. For the modal analysis, a finite element (FE) model is developed where a representative volume element (RVE) analysis is also included to properly consider the influence of the microstructure. The experimental and numerical results are compared and validated. Moreover, an estimation model is proposed for a type of coil with different fiber lengths. Finally, the estimated coil set is produced and tested employing the same methodology in order to illustrate the capacity of the developed framework.

Characterization of the Ejector Pump Performance for the Assisted Bidirectional Glenn Procedure

This study introduces an algebraic model informed by computational fluid dynamics (CFD) simulations to investigate the performance of the assisted bidirectional Glenn (ABG) operation on a broad range of conditions. The performance of this operation, as measured by the superior vena cava (SVC) pressure, depends on the nozzle area in its ejector pump and the patient’s pulmonary vascular resistance (PVR). Using the developed algebraic model to explore this two-dimensional parameter space shows that the ejector pump can create a pressure difference between the pulmonary artery and the SVC as high as 5 mmHg. The lowest SVC pressure is produced at a nozzle area that decreases linearly with the PVR such that, at PVR =4.2 (Wood units-m2), there is no added benefit in utilizing the ejector pump effect (optimal nozzle area is zero, corresponding to the bidirectional Glenn circulation). At PVR =2 (Wood units-m2), the SVC pressure can be lowered to less than 4 mmHg by using an optimal nozzle area of ≈2.5 mm2. Regardless of the PVR, adding a 2 mm2 nozzle to the baseline bidirectional Glenn boosts the oxygen saturation and delivery by at least 15%. The SVC pressure for that 2 mm2 nozzle remains below 14 mmHg for all PVRs less than 7 Wood units-m2. The mechanical efficiency of the optimal designs consistently remains below 30%, indicating the potential for improvement in the future. A good agreement is observed between the algebraic model and high-fidelity CFD simulations.

Manipulation of free-floating objects using Faraday flows and deep reinforcement learning

The ability to remotely control a free-floating object through surface flows on a fluid medium can facilitate numerous applications. Current studies on this problem have been limited to uni-directional motion control due to the challenging nature of the control problem. Analytical modelling of the object dynamics is difficult due to the high-dimensionality and mixing of the surface flows while the control problem is hard due to the nonlinear slow dynamics of the fluid medium, underactuation, and chaotic regions. This study presents a methodology for manipulation of free-floating objects using large-scale physical experimentation and recent advances in deep reinforcement learning. We demonstrate our methodology through the open-loop control of a free-floating object in water using a robotic arm. Our learned control policy is relatively quick to obtain, highly data efficient, and easily scalable to a higher-dimensional parameter space and/or experimental scenarios. Our results show the potential of data-driven approaches for solving and analyzing highly complex nonlinear control problems.

Towards an Efficient Validation of Dynamical Whole-brain Models

Simulating the resting-state brain dynamics via mathematical whole-brain models requires an optimal selection of parameters, which determine the model’s capability to replicate empirical data. Since the parameter optimization via a grid search (GS) becomes unfeasible for high-dimensional models, we evaluate several alternative approaches to maximize the correspondence between simulated and empirical functional connectivity. A dense GS serves as a benchmark to assess the performance of four optimization schemes: Nelder-Mead Algorithm (NMA), Particle Swarm Optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMAES) and Bayesian Optimization (BO). To compare them, we employ an ensemble of coupled phase oscillators built upon individual empirical structural connectivity of 105 healthy subjects. We determine optimal model parameters from two- and three-dimensional parameter spaces and show that the overall fitting quality of the tested methods can compete with the GS. There are, however, marked differences in the required computational resources and stability properties, which we also investigate before proposing CMAES and BO as efficient alternatives to a high-dimensional GS. For the three-dimensional case, these methods generated similar results as the GS, but within less than 6% of the computation time. Our results contribute to an efficient validation of models for personalized simulations of brain dynamics.

A Model for Integrated Inventory and Assortment Planning

Integrating inventory and assortment planning decisions is a challenging task that requires comparing the value of demand expansion through broader choice for consumers with the value of higher in-stock availability. We develop a stockout-based substitution model for trading off these values in a setting with inventory replenishment, a feature missing in the literature. Using the closed form solution for the single-product case, we develop an accurate approximation for the multiproduct case. This approximated formulation allows us to optimize inventory decisions by solving a fractional integer program with a fixed point equation constraint. When products have equal margins, we solve the integer program exactly by bisection over a one-dimensional parameter. In contrast, when products have different margins, we propose a fractional relaxation that we can also solve by bisection and that results in near-optimal solutions. Overall, our approach provides solutions within 0.1% of the optimal policy and finds the optimal solution in 80% of the random instances we generate. This paper was accepted by David Simchi-Levi, optimization.

Data-driven discovery of dimensionless numbers and scaling laws from experimental measurements

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a highly-multivariable system with incomplete governing equations. In this study, we embed the principle of dimensional invariance into a two-level machine learning scheme to automatically discover dominant and unique dimensionless numbers and scaling laws from data. The proposed methodology, called dimensionless learning, can be treated as a physics-based dimension reduction. It can reduce high-dimensional parameter spaces into descriptions involving just a few physically-interpretable dimensionless parameters, which significantly simplifies the process design and optimization of the system. We demonstrate the algorithm by solving several challenging engineering problems with noisy experimental measurements (not synthetic data) collected from the literature. The examples include turbulent Rayleigh-Bénard convection, vapor depression dynamics in laser melting of metals, and porosity formation in 3D printing. We also show that the proposed approach can identify dimensionally homogeneous differential equations with minimal parameters by leveraging sparsity-promoting techniques.

Emulator-based Bayesian optimization for efficient multi-objective calibration of an individual-based model of malaria

Individual-based models have become important tools in the global battle against infectious diseases, yet model complexity can make calibration to biological and epidemiological data challenging. We propose using a Bayesian optimization framework employing Gaussian process or machine learning emulator functions to calibrate a complex malaria transmission simulator. We demonstrate our approach by optimizing over a high-dimensional parameter space with respect to a portfolio of multiple fitting objectives built from datasets capturing the natural history of malaria transmission and disease progression. Our approach quickly outperforms previous calibrations, yielding an improved final goodness of fit. Per-objective parameter importance and sensitivity diagnostics provided by our approach offer epidemiological insights and enhance trust in predictions through greater interpretability.

On geometry parameterization for simulation-driven design closure of antenna structures

Full-wave electromagnetic (EM) simulation tools have become ubiquitous in antenna design, especially final tuning of geometry parameters. From the reliability standpoint, the recommended realization of EM-driven design is through rigorous numerical optimization. It is a challenging endeavor with the major issues related to the high computational cost of the process, but also the necessity of handling several objectives and constraints over often highly-dimensional parameter spaces. From the numerical perspective, making decisions about the formulation of the optimization problem, the approach to handling the design constraints, but also parameterization of the antenna geometry, are all non-trivial. At the same time, these issues are interleaved, and may play an important role in the performance and reliability of the simulation-based design closure process. This paper demonstrates that the approach to arranging the structure parameterization (e.g., the use of absolute or relative parameters) may have a major effect of the optimization outcome. Our investigations are carried out using three broadband monopole antennas optimized under different scenarios and using different parameterizations. In particular, the results indicate that relative parameterization is preferred for optimization of input characteristics, whereas absolute parameterization is more suitable for size reduction.

Efficient sampling of constrained high-dimensional theoretical spaces with machine learning

Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental results project onto a subspace of parameters that are consistent with those observations, but mapping these constraints to the underlying parameters is also typically intractable. Instead, physicists often resort to scanning small subsets of the full parameter space and testing for experimental consistency. We propose an alternative approach that uses generative models to significantly improve the computational efficiency of sampling high-dimensional parameter spaces. To demonstrate this, we sample the constrained and phenomenological Minimal Supersymmetric Standard Models subject to the requirement that the sampled points are consistent with the measured Higgs boson mass. Our method achieves orders of magnitude improvements in sampling efficiency compared to a brute force search.

Resonant leptogenesis and TM$$_1$$ mixing in minimal type-I seesaw model with S$$_4$$ symmetry

We present an S$$_4$$ 4 flavour symmetric model within a minimal seesaw framework resulting in mass matrices that leads to TM$$_1$$ 1 mixing. Minimal seesaw is realized by adding two right-handed neutrinos to the Standard Model. The model predicts Normal Hierarchy (NH) for neutrino masses. Using the constrained six-dimensional parameter space of the model, we have evaluated the effective Majorana neutrino mass, which is the parameter of interest in neutrinoless double beta decay experiments. The possibility of explaining baryogenesis via resonant leptogenesis is also examined within the model. A non-zero, resonantly enhanced CP asymmetry generated from the decay of right-handed neutrinos at the TeV scale is studied, considering flavour effects. The evolution of lepton asymmetry is discussed by solving the set of Boltzmann equations numerically and obtain the value of baryon asymmetry to be $$|\eta _B| = 6.3 \times 10^{-10}$$ | η B | = 6.3 × 10 - 10 with the choice of right-handed neutrino mass, $$M_1 = 10$$ M 1 = 10 TeV and mass splitting, $$d \simeq 10^{-8}$$ d ≃ 10 - 8 .