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

Application of the immunoregulatory receptor LILRB1 as a crystallisation chaperone for human class I MHC complexes

X-ray crystallographic studies of class I peptide-MHC molecules (pMHC) continue to provide important insights into immune recognition, however their success depends on generation of diffraction-quality crystals, which remains a significant challenge. While protein engineering techniques such as surface-entropy reduction and lysine methylation have proven utility in facilitating and/or improving protein crystallisation, they risk affecting the conformation and biochemistry of the class I MHC antigen binding groove. An attractive alternative is the use of noncovalent crystallisation chaperones, however these have not been developed for pMHC. Here we describe a method for promoting class I pMHC crystallisation, by exploiting its natural ligand interaction with the immunoregulatory receptor LILRB1 as a novel crystallisation chaperone. First, focussing on a model HIV-1-derived HLA-A2-restricted peptide, we determined a 2.4 Å HLA-A2/LILRB1 structure, which validated that co crystallisation with LILRB1 does not alter conformation of the antigenic peptide. We then demonstrated that addition of LILRB1 enhanced the crystallisation of multiple peptide-HLA-A2 complexes, and identified a generic condition for initial co-crystallisation. LILRB1 chaperone-based crystallisation enabled structure determination for HLA-A2 complexes previously intransigent to crystallisation, including both conventional and post-translationally-modified peptides, of diverse lengths. Since both the LILRB1 recognition interface on the HLA-A2 α3 domain molecule and HLA-A2 mediated crystal contacts are predominantly conserved across class I MHC molecules, the approach we outline could prove applicable to a diverse range of class I pMHC. LILRB1 chaperone-mediated crystallisation should expedite molecular insights into the immunobiology of diverse immune-related diseases and immunotherapeutic strategies, particularly involving class I pMHC complexes that are challenging to crystallise

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

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

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