Population pharmacokinetic model selection assisted by machine learning.

A fit-for-purpose structural and statistical model is the first major requirement in population pharmacometric model development. In this manuscript we discuss how this complex and computationally intensive task could benefit from supervised machine learning algorithms. We compared the classical pharmacometric approach with two machine learning methods, genetic algorithm and neural networks, in different scenarios based on simulated pharmacokinetic data. Genetic algorithm performance was assessed using a fitness function based on log-likelihood, whilst neural networks were trained using mean square error or binary cross-entropy loss. Machine learning provided a selection based only on statistical rules and achieved accurate selection. The minimization process of genetic algorithm was successful at allowing the algorithm to select plausible models. Neural network classification tasks achieved the most accurate results. Neural network regression tasks were less precise than neural network classification and genetic algorithm methods. The computational gain obtained by using machine learning was substantial, especially in the case of neural networks. We demonstrated that machine learning methods can greatly increase the efficiency of pharmacokinetic population model selection in case of large datasets or complex models requiring long run-times. Our results suggest that machine learning approaches can achieve a first fast selection of models which can be followed by more conventional pharmacometric approaches.

Reduced basis methods for numerical room acoustic simulations with parametrized boundaries.

The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis method (RBM) to achieve a computational cost reduction relative to a traditional full-order model (FOM) for wave-based room acoustic simulations with parametrized boundaries. The FOM solver is based on the spectral-element method; however, other numerical methods could be applied. The RBM reduces the computational burden by solving the problem in a low-dimensional subspace for parametrized frequency-independent and frequency-dependent boundary conditions. The problem is formulated in the Laplace domain, which ensures the stability of the reduced-order model (ROM). We study the potential of the proposed RBM in terms of computational efficiency, accuracy, and storage requirements, and we show that the RBM leads to 100-fold speedups for a two-dimensional case and 1000-fold speedups for a three-dimensional case with an upper frequency of 2 and 1 kHz, respectively. While the FOM simulations needed to construct the ROM are expensive, we demonstrate that the ROM has the potential of being 3 orders of magnitude faster than the FOM when four different boundary conditions are simulated per room surface.

Fast screening of covariates in population models empowered by machine learning.

One of the objectives of Pharmacometry (PMX) population modeling is the identification of significant and clinically relevant relationships between parameters and covariates. Here, we demonstrate how this complex selection task could benefit from supervised learning algorithms using importance scores. We compare various classical methods with three machine learning (ML) methods applied to NONMEM empirical Bayes estimates: random forest, neural networks (NNs), and support vector regression (SVR). The performance of the ML models is assessed using receiver operating characteristic (ROC) curves. The F1 score, which measures test accuracy, is used to compare ML and PMX approaches. Methods are applied to different scenarios of covariate influence based on simulated pharmacokinetics data. ML achieved similar or better F1 scores than stepwise covariate modeling (SCM) and conditional sampling for stepwise approach based on correlation tests (COSSAC). Correlations between covariates and the number of false covariates does not affect the performance of any method, but effect size has an impact. Methods are not equivalent with respect to computational speed; SCM is 30 and 100-times slower than NN and SVR, respectively. The results are validated in an additional scenario involving 100 covariates. Taken together, the results indicate that ML methods can greatly increase the efficiency of population covariate model building in the case of large datasets or complex models that require long run-times. This can provide fast initial covariate screening, which can be followed by more conventional PMX approaches to assess the clinical relevance of selected covariates and build the final model.

Modeling synchronization in globally coupled oscillatory systems using model order reduction.

We construct reduced order models for two classes of globally coupled multi-component oscillatory systems, selected as prototype models that exhibit synchronization. These are the Kuramoto model, considered both in its original formulation and with a suitable change of coordinates, and a model for the circadian clock. The systems of interest possess strong reduction properties, as their dynamics can be efficiently described with a low-dimensional set of coordinates. Specifically, the solution and selected quantities of interest are well approximated at the reduced level, and the reduced models recover the expected transition to synchronized states as the coupling strengths vary. Assuming that the interactions depend only on the averages of the system variables, the surrogate models ensure a significant computational speedup for large systems.

Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method.

An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at fluid-solid interface require continuity of the normal component of particle velocity and traction, whereas the tangential components vanish. A main challenge is to model interface waves, namely, the Scholte and leaky Rayleigh waves. This study uses a nodal discontinuous Galerkin (dG) finite-element method with the medium discretized using an unstructured uniform triangular meshes. The natural boundary conditions in the dG method are implemented by (1) using an explicit upwind numerical flux and (2) by using an implicit penalty flux and setting the modulus of rigidity of the acoustic medium to zero. The accuracy of these methods is evaluated by comparing the numerical solutions with analytical ones, with source and receiver at and away from the interface. The study shows that the solutions obtained from the explicit and implicit boundary conditions provide the correct results. The stability of the dG scheme is determined by the numerical flux, which also implements the boundary conditions by unifying the numerical solution at shared edges of the elements in an energy stable manner.

Time-domain room acoustic simulations with extended-reacting porous absorbers using the discontinuous Galerkin method.

This paper presents an equivalent fluid model (EFM) formulation in a three-dimensional time-domain discontinuous Galerkin finite element method framework for room acoustic simulations. Using the EFM allows for the modeling of the extended-reaction (ER) behavior of porous sound absorbers. The EFM is formulated in the numerical framework by using the method of auxiliary differential equations to account for the frequency dependent dissipation of the porous material. The formulation is validated analytically and an excellent agreement with the theory is found. Experimental validation for a single reflection case is also conducted, and it is shown that using the EFM improves the simulation accuracy when modeling a porous material backed by an air cavity as compared to using the local-reaction (LR) approximation. Last, a comparative study of different rooms with different porous absorbers is presented, using different boundary modeling techniques, namely, a LR approximation, a field-incidence (FI) approximation, or modeling the full ER behavior with the EFM. It is shown that using a LR or FI approximation leads to large and perceptually noticeable errors in simulated room acoustic parameters. The average T20 reverberation time error is 4.3 times the just-noticeable-difference (JND) threshold when using LR and 2.9 JND when using FI.

Time domain room acoustic simulations using the spectral element method.

This paper presents a wave-based numerical scheme based on a spectral element method, coupled with an implicit-explicit Runge-Kutta time stepping method, for simulating room acoustics in the time domain. The scheme has certain features which make it highly attractive for room acoustic simulations, namely (a) its low dispersion and dissipation properties due to a high-order spatio-temporal discretization; (b) a high degree of geometric flexibility, where adaptive, unstructured meshes with curvilinear mesh elements are supported; and (c) its suitability for parallel implementation on modern many-core computer hardware. A method for modelling locally reacting, frequency dependent impedance boundary conditions within the scheme is developed, in which the boundary impedance is mapped to a multipole rational function and formulated in differential form. Various numerical experiments are presented, which reveal the accuracy and cost-efficiency of the proposed numerical scheme.

Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography.

The feasibility of data based machine learning applied to ultrasound tomography is studied to estimate water-saturated porous material parameters. In this work, the data to train the neural networks is simulated by solving wave propagation in coupled poroviscoelastic-viscoelastic-acoustic media. As the forward model, a high-order discontinuous Galerkin method is considered, while deep convolutional neural networks are used to solve the parameter estimation problem. In the numerical experiment, the material porosity and tortuosity is estimated, while the remaining parameters which are of less interest are successfully marginalized in the neural networks-based inversion. Computational examples confirm the feasibility and accuracy of this approach.

Reduced basis catalogs for gravitational wave templates.

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for nonspinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about 10-10(5) fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.

Two-Dimensional RBF-ENO Method on Unstructured Grids.

Essentially non-oscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well studied. We propose a high-order ENO method based on radial basis function (RBF) to solve hyperbolic conservation laws on general two-dimensional grids. The radial basis function reconstruction offers a flexible way to deal with ill-conditioned cell constellations. We introduce a smoothness indicator based on RBFs and a stencil selection algorithm suitable for general meshes. Furthermore, we develop a stable method to evaluate the RBF reconstruction in the finite volume setting which circumvents the stagnation of the error and keeps the condition number of the reconstruction bounded. We conclude with several challenging numerical examples in two dimensions to show the robustness of the method.