Dynamic data-driven model reduction: adapting reduced models from incomplete data

This work presents a data-driven online adaptive model reduction approach for systems that undergo dynamic changes. Classical model reduction constructs a reduced model of a large-scale system in an offline phase and then keeps the reduced model unchanged during the evaluations in an online phase; however, if the system changes online, the reduced model may fail to predict the behavior of the changed system. Rebuilding the reduced model from scratch is often too expensive in time-critical and real-time environments. We introduce a dynamic data-driven adaptation approach that adapts the reduced model from incomplete sensor data obtained from the system during the online computations. The updates to the reduced models are derived directly from the incomplete data, without recourse to the full model. Our adaptivity approach approximates the missing values in the incomplete sensor data with gappy proper orthogonal decomposition. These approximate data are then used to derive low-rank updates to the reduced basis and the reduced operators. In our numerical examples, incomplete data with 30–40 % known values are sufficient to recover the reduced model that would be obtained via rebuilding from scratch.United States. Air Force Office of Scientific Research (AFOSR MURI on multi-information sources of multi-physics systems, Award Number FA9550-15-1-0038)United States. Dept. of Energy (Applied Mathematics Program, Award DE-FG02 08ER2585)United States. Dept. of Energy (Applied Mathematics Program, Award DE-SC0009297

Data-Driven Reduced Model Construction with Time-Domain Loewner Models

This work presents a data-driven nonintrusive model reduction approach for large-scale time-dependent systems with linear state dependence. Traditionally, model reduction is performed in an intrusive projection-based framework, where the operators of the full model are required either explicitly in an assembled form or implicitly through a routine that returns the action of the operators on a vector. Our nonintrusive approach constructs reduced models directly from trajectories of the inputs and outputs of the full model, without requiring the full-model operators. These trajectories are generated by running a simulation of the full model; our method then infers frequency-response data from these simulated time-domain trajectories and uses the data-driven Loewner framework to derive a reduced model. Only a single time-domain simulation is required to derive a reduced model with the new data-driven nonintrusive approach. We demonstrate our model reduction method on several benchmark examples and a finite element model of a cantilever beam; our approach recovers the classical Loewner reduced models and, for these problems, yields high-quality reduced models despite treating the full model as a black box. Key words: data-driven model reduction, nonintrusive model reduction, projection-based reduced models, Loewner framework, black-box models, dynamical systems, partial differential equationsNational Science Foundation (U.S.) (Award 1507488

Optimal Model Management for Multifidelity Monte Carlo Estimation

This work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high-fidelity models. Existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs; however, a general collection of surrogate models, which may include projection-based reduced models, data-fit models, support vector machines, and simplified-physics models, does not necessarily give rise to such a hierarchy. Our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type. Instead of relying on error and cost rates, an optimization problem balances the number of model evaluations across the high-fidelity and surrogate models with respect to error and costs. We show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models. Our multifidelity method makes occasional recourse to the high-fidelity model; in doing so it provides an unbiased estimator of the statistics of the high-fidelity model, even in the absence of error bounds and error estimators for the surrogate models. Numerical experiments with linear and nonlinear examples show that speedups by orders of magnitude are obtained compared to Monte Carlo estimation that invokes a single model only

Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models

We consider control and stabilization for large-scale dynamical systems with uncertain, time-varying parameters. The time-critical task of controlling a dynamical system poses major challenges: using large-scale models is prohibitive, and accurately inferring parameters can be expensive, too. We address both problems by proposing an offine-online strategy for controlling systems with time- varying parameters. During the offine phase, we use a high-fidelity model to compute a library of optimal feedback controller gains over a sampled set of parameter values. Then, during the online phase, in which the uncertain parameter changes over time, we learn a reduced-order model from system data. The learned reduced-order model is employed within an optimization routine to update the feedback control throughout the online phase. Since the system data naturally reects the uncertain parameter, the data-driven updating of the controller gains is achieved without an explicit parameter estimation step. We consider two numerical test problems in the form of partial differential equations: a convection-diffusion system, and a model for ow through a porous medium. We demonstrate on those models that the proposed method successfully stabilizes the system model in the presence of process noise.DARPA EQUiPS program (award number UTA15-001067)United States. Department of Energy. Office of Advanced Scientific Computing Research (grant DE-FG02-08ER2585)United States. Department of Energy. Office of Advanced Scientific Computing Research (grant DE-SC000929

Multifidelity Monte Carlo estimation for large-scale uncertainty propagation

One important task of uncertainty quantification is propagating input uncertainties through a system of interest to quantify the uncertainties’ effects on the system outputs; however, numerical methods for uncertainty propagation are often based on Monte Carlo estimation, which can require large numbers of numerical simulations of the numerical model describing the system response to obtain estimates with acceptable accuracies. Thus, if the model is computationally expensive to evaluate, then Monte-Carlo-based uncertainty propagation methods can quickly become computationally intractable. We demonstrate that multifidelity methods can significantly speedup uncertainty propagation by leveraging low-cost low-fidelity models and establish accuracy guarantees by using occasional recourse to the expensive high-fidelity model. We focus on the multifidelity Monte Carlo method, which is a multifidelity approach that optimally distributes work among the models such that the mean-squared error of the multifidelity estimator is minimized for a given computational budget. The multifidelity Monte Carlo method is applicable to general types of low-fidelity models, including projection-based reduced models, data-fit surrogates, response surfaces, and simplified-physics models. We apply the multifidelity Monte Carlo method to a coupled aero-structural analysis of a wing and a flutter problem with a high-aspect-ratio wing. The low-fidelity models are data-fit surrogate models derived with standard procedures that are built in common software environments such as Matlab and numpy/scipy. Our results demonstrate speedups of orders of magnitude compared to using the high-fidelity model alone.United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (Award FA9550-15-1-0038

Modifications outside CDR1, 2 and 3 of the TCR variable β domain increase TCR expression and antigen-specific function

T cell receptor (TCR) gene modified T cells are a promising form of adoptive cellular therapy against human malignancies and viral infections. Since the first human clinical trial was carried out in 2006, several strategies have been developed to improve the efficacy and safety of TCR engineered T cells by enhancing the surface expression of the introduced therapeutic TCRs whilst reducing the mis-pairing with endogenous TCR chains. In this study, we explored how modifications of framework residues in the TCR variable domains affect TCR expression and function. We used bioinformatic and protein structural analyses to identify candidate amino acid residues in the framework of the variable β domain predicted to drive high TCR surface expression. Changes of these residues in poorly expressed TCRs resulted in improved surface expression and boosted target cell specific killing by engineered T cells expressing the modified TCRs. Overall, these results indicate that small changes in the framework of the TCR variable domains can result in improved expression and functionality, while at the same time reducing the risk of toxicity associated with TCR mis-pairing

Phosphonodiamidate prodrugs of phosphoantigens (ProPAgens) exhibit potent Vγ9/Vδ2 T cell activation and eradication of cancer cells

The phosphoantigen (E)-4-hydroxy-3-methyl-but-2-enyl pyrophosphate (HMBPP) is an established activator of Vγ9/Vδ2 T cells and stimulates downstream effector functions including cytotoxicity and cytokine production. In order to improve its drug-like properties, we herein report the design, synthesis, serum stability, in vitro metabolism, and biological evaluation of a new class of symmetrical phosphonodiamidate prodrugs of methylene and difluoromethylene monophosphonate derivatives of HMBPP. These prodrugs, termed phosphonodiamidate ProPAgens, were synthesized in good yields, exhibited excellent serum stability (>7 h), and their in vitro metabolism was shown to be initiated by carboxypeptidase Y. These phosphonodiamidate ProPAgens triggered potent activation of Vγ9/Vδ2 T cells, which translated into efficient Vγ9/Vδ2 T cell-mediated eradication of bladder cancer cells in vitro. Together, these findings showcase the potential of these phosphonodiamidate ProPAgens as Vγ9/Vδ2 T cell modulators that could be further developed as novel cancer immunotherapeutic agents