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Richard D. Braatz

Publications and source records attributed to Richard D. Braatz.

At least 55 records · Page 3Linked to original sources
arXiv2024

An Integrated Experimental and Modeling Approach for Crystallization of Complex Biotherapeutics

Crystallization of proteins, specifically proteins of medical relevance, is performed for various reasons such as to understand the protein structure and to design therapies. Obtaining kinetic constants in rate laws for nucleation and growth of advanced biotherapeutics such as capsids, an assembly of macromolecules, is challenging and essential to the design of the crystallization processes. In this work, coupled population balance and species balance equations are developed to extract nucleation and growth kinetics for crystallization of recombinant adeno-associated virus (rAAV) capsids. A comparison of model results with that of experimental data for capsid crystallization in hanging-drop vapor diffusion system shows that slow rate of vapor diffusion from the droplet controls the initial nucleation and growth processes, and the capsid nucleation occurs via heterogeneous nucleation in the microdroplet. Results also show that the capsids, which are of very high molecular weight (~3.6 MDa), have a similar tendency to nucleate as small organic molecules such as glycine (75 Da), low-molecular-weight proteins, and small-molecule active pharmaceutical ingredients due to its ball-shaped outer structure/shape. Capids also show a prolonged nucleation period as for proteins and other macromolecules, but has a slow growth rate with a growth rate pre-factor seven orders of magnitude smaller than that of lysozyme. The capsid crystal growth rate is weakly sensitive to the supersaturation compared to lysozyme and is limited by the transport of capsids due to slow Brownian motion resulting from the very high molecular weight.

physics.app-ph↗
arXiv2024

Selective Enrichment of Full AAV Capsids

Gene therapies using recombinant adeno-associated virus (rAAV) have been developed to treat monogenic and acquired diseases but are currently the most expensive drugs due, in part, to high manufacturing costs. The cells producing rAAV generate substantial quantities of empty (50-90%) and partially filled capsids that must be removed prior to final formulation. The conventional separation processes are inefficient in removing empty and partially filled capsids, have low yield, scale poorly, time consuming and need additional purification steps. This article demonstrates one step separation of full capsids from a mixture of full, partially filled, and empty capsids, and other protein impurities using selective crystallization, a purification process, which is first time in protein purification and is performed without physically or chemically modifying the target component for the first time in the history of selective crystallization, and is highly-efficient, highly-scalable, and economical. Hanging-drop vapor diffusion experiments were used to scout crystallization conditions in which full and empty capsids crystallize, then to define conditions in which crystals of full, empty, or both full and empty capsids nucleate and grow. The experimental results for rAAV serotypes 5, 8, and 9 as exemplary vectors and scale-up results show that full capsids can be selectively crystallized and separated in one step from a mixture of full, partially filled, and empty capsids, and other proteins with full capsid enrichment of greater than 80%, approximately 20% higher, and yield of greater than 90%, approximately greater than 30% higher from the existing methods, keeping their biological activity intact, in a short period of time (less than 4 h), with approximately 87% reduction in processing time from the existing processing time and without the need of additional purification steps and in one round.

physics.med-ph↗
arXiv2024

Gaussian process-based online health monitoring and fault analysis of lithium-ion battery systems from field data

Health monitoring, fault analysis, and detection are critical for the safe and sustainable operation of battery systems. We apply Gaussian process resistance models on lithium iron phosphate battery field data to effectively separate the time-dependent and operating point-dependent resistance. The data set contains 29 battery systems returned to the manufacturer for warranty, each with eight cells in series, totaling 232 cells and 131 million data rows. We develop probabilistic fault detection rules using recursive spatiotemporal Gaussian processes. These processes allow the quick processing of over a million data points, enabling advanced online monitoring and furthering the understanding of battery pack failure in the field. The analysis underlines that often, only a single cell shows abnormal behavior or a knee point, consistent with weakest-link failure for cells connected in series, amplified by local resistive heating. The results further the understanding of how batteries degrade and fail in the field and demonstrate the potential of efficient online monitoring based on data. We open-source the code and publish the large data set upon completion of the review of this article.

cs.LG↗
arXiv2024

Systematic Feature Design for Cycle Life Prediction of Lithium-Ion Batteries During Formation

Optimization of the formation step in lithium-ion battery manufacturing is challenging due to limited physical understanding of solid electrolyte interphase formation and the long testing time (~100 days) for cells to reach the end of life. We propose a systematic feature design framework that requires minimal domain knowledge for accurate cycle life prediction during formation. Two simple Q(V) features designed from our framework, extracted from formation data without any additional diagnostic cycles, achieved a median of 9.20% error for cycle life prediction, outperforming thousands of autoML models using pre-defined features. We attribute the strong performance of our designed features to their physical origins - the voltage ranges identified by our framework capture the effects of formation temperature and microscopic particle resistance heterogeneity. By designing highly interpretable features, our approach can accelerate formation research, leveraging the interplay between data-driven feature design and mechanistic understanding.

cs.LG↗
arXiv2024

Safe Learning-Based Optimization of Model Predictive Control: Application to Battery Fast-Charging

Model predictive control (MPC) is a powerful tool for controlling complex nonlinear systems under constraints, but often struggles with model uncertainties and the design of suitable cost functions. To address these challenges, we discuss an approach that integrates MPC with safe Bayesian optimization to optimize long-term closed-loop performance despite significant model-plant mismatches. By parameterizing the MPC stage cost function using a radial basis function network, we employ Bayesian optimization as a multi-episode learning strategy to tune the controller without relying on precise system models. This method mitigates conservativeness introduced by overly cautious soft constraints in the MPC cost function and provides probabilistic safety guarantees during learning, ensuring that safety-critical constraints are met with high probability. As a practical application, we apply our approach to fast charging of lithium-ion batteries, a challenging task due to the complicated battery dynamics and strict safety requirements, subject to the requirement to be implementable in real time. Simulation results demonstrate that, in the context of model-plant mismatch, our method reduces charging times compared to traditional MPC methods while maintaining safety. This work extends previous research by emphasizing closed-loop constraint satisfaction and offers a promising solution for enhancing performance in systems where model uncertainties and safety are critical concerns.

eess.SY↗
arXiv2024

HEK-Omics: The promise of omics to optimize HEK293 for recombinant adeno-associated virus (rAAV) gene therapy manufacturing

Gene therapy is poised to transition from niche to mainstream medicine, with recombinant adeno-associated virus (rAAV) as the vector of choice. However, this requires robust, scalable, industrialized production to meet demand and provide affordable patient access, which has thus far failed to materialize. Closing the chasm between demand and supply requires innovation in biomanufacturing to achieve the essential step change in rAAV product yield and quality. Omics provides a rich source of mechanistic knowledge that can be applied to HEK293, the prevailing cell line for rAAV production. In this review, the findings from a growing number of disparate studies that apply genomics, epigenomics, transcriptomics, proteomics, and metabolomics to HEK293 bioproduction are explored. Learnings from CHO-Omics, application of omics approaches to improve CHO bioproduction, provide context for the potential of "HEK-Omics" as a multiomics-informed approach providing actionable mechanistic insights for improved transient and stable production of rAAV and other recombinant products in HEK293.

q-bio.GN↗
arXiv2024

A Parallel Vector-form $LDL^\top$ Decomposition for Accelerating Execution-time-certified $\ell_1$-penalty Soft-constrained MPC

Handling possible infeasibility and providing an execution time certificate are two pressing requirements of real-time Model Predictive Control (MPC). To meet these two requirements simultaneously, this paper proposes an $\ell_1$-penalty soft-constrained MPC formulation that is globally feasible and solvable with an execution time certificate using our proposed algorithm. This paper proves for the first time that $\ell_1$-penalty soft-constrained MPC problems can be equivalently transformed into a box-constrained quadratic programming (Box-QP) and then our previous execution-time-certified algorithm \cite{wu2023direct} (only limited to Box-QP) can be applied. However, our previous Box-QP algorithm \cite{wu2023direct}, which provides a theoretical execution-time certificate, is conservative in its iteration analysis, thus sacrificing computation efficiency. To this end, this paper proposes a novel $LDL^\top$ decomposition for the first time, to accelerate the computation of Newton step at each iteration. The speedup of our $LDL^\top$ decomposition comes from two-fold: \textit{i)} exploitation of the fact that the number of inequality constraints is generally larger than the number of variables in condensed MPC formulations, \textit{ii)} vectorized and parallel implementation based on based on its vector-wise operations, instead of element-wise operations of previous decomposition methods. Numerical experiments demonstrate great speedups of the proposed $LDL^\top$ decomposition (even up to 1000-fold, compared to the standard Choleksky method), which thus helps our solver achieve comparable computation performance to the state-of-the-art solvers such as IPOPT and OSQP. Code is available at \url{https://github.com/liangwu2019/L1-penalty-QP}.

eess.SY↗
arXiv2024

Mechanistic Modeling and Analysis of Thermal Radiation in Conventional, Microwave-assisted, and Hybrid Freeze Drying for Biopharmaceutical Manufacturing

In freeze drying, thermal radiation has a significant effect on the drying process of vials located near the corner and edge of the trays, resulting in non-uniformity of the products. Understanding and being able to predict the impact of thermal radiation are therefore critical to accurate determination of the drying process endpoint given the variation in heat transfer of each vial. This article presents a new mechanistic model that describes complex thermal radiation during primary drying in conventional, microwave-assisted, and hybrid freeze drying. Modeling of thermal radiation employs the diffuse gray surface model and radiation network approach, which systematically and accurately incorporates simultaneous radiation exchange between every surface including the chamber wall and vials, allowing the framework to be seamlessly applied for analyzing various freeze-dryer designs. Model validation with data from the literature shows accurate prediction of the drying times for all vials, including inner, edge, and corner vials. The validated model is demonstrated for thermal radiation analysis and parametric studies to guide the design and optimization of freeze dryers.

cs.CE↗
arXiv2024

A nonparametric learning framework for nonlinear robust output regulation

A nonparametric learning solution framework is proposed for the global nonlinear robust output regulation problem. We first extend the assumption that the steady-state generator is linear in the exogenous signal to the more relaxed assumption that it is polynomial in the exogenous signal. Additionally, a nonparametric learning framework is proposed to eliminate the construction of an explicit regressor, as required in the adaptive method, which can potentially simplify the implementation and reduce the computational complexity of existing methods. With the help of the proposed framework, the robust nonlinear output regulation problem can be converted into a robust non-adaptive stabilization problem for the augmented system with integral input-to-state stable (iISS) inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. Furthermore, we apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without the need for adaptive parametric techniques. An explicit nonlinear mapping can directly provide the estimated parameters, which will exponentially converge to the unknown frequencies. Finally, a feedforward control design is proposed to solve the linear output regulation problem using the nonparametric learning framework. Two simulation examples are provided to illustrate the effectiveness of the theoretical results.

eess.SY↗
arXiv2024

Accounting for the Effects of Probabilistic Uncertainty During Fast Charging of Lithium-ion Batteries

Batteries are nonlinear dynamical systems that can be modeled by Porous Electrode Theory models. The aim of optimal fast charging is to reduce the charging time while keeping battery degradation low. Most past studies assume that model parameters and ambient temperature are a fixed known value and that all PET model parameters are perfectly known. In real battery operation, however, the ambient temperature and the model parameters are uncertain. To ensure that operational constraints are satisfied at all times in the context of model-based optimal control, uncertainty quantification is required. Here, we analyze optimal fast charging for modest uncertainty in the ambient temperature and 23 model parameters. Uncertainty quantification of the battery model is carried out using non-intrusive polynomial chaos expansion and the results are verified with Monte Carlo simulations. The method is investigated for a constant current--constant voltage charging strategy for a battery for which the strategy is known to be standard for fast charging subject to operating below maximum current and charging constraints. Our results demonstrate that uncertainty in ambient temperature results in violations of constraints on the voltage and temperature. Our results identify a subset of key parameters that contribute to fast charging among the overall uncertain parameters. Additionally, it is shown that the constraints represented by voltage, temperature, and lithium-plating overpotential are violated due to uncertainties in the ambient temperature and parameters. The C-rate and charge constraints are then adjusted so that the probability of violating the degradation acceleration condition is below a pre-specified value. This approach demonstrates a computationally efficient approach for determining fast-charging protocols that take probabilistic uncertainties into account.

eess.SY↗
arXiv2024

Learning Model Predictive Control Parameters via Bayesian Optimization for Battery Fast Charging

Tuning parameters in model predictive control (MPC) presents significant challenges, particularly when there is a notable discrepancy between the controller's predictions and the actual behavior of the closed-loop plant. This mismatch may stem from factors like substantial model-plant differences, limited prediction horizons that do not cover the entire time of interest, or unforeseen system disturbances. Such mismatches can jeopardize both performance and safety, including constraint satisfaction. Traditional methods address this issue by modifying the finite horizon cost function to better reflect the overall operational cost, learning parts of the prediction model from data, or implementing robust MPC strategies, which might be either computationally intensive or overly cautious. As an alternative, directly optimizing or learning the controller parameters to enhance closed-loop performance has been proposed. We apply Bayesian optimization for efficient learning of unknown model parameters and parameterized constraint backoff terms, aiming to improve closed-loop performance of battery fast charging. This approach establishes a hierarchical control framework where Bayesian optimization directly fine-tunes closed-loop behavior towards a global and long-term objective, while MPC handles lower-level, short-term control tasks. For lithium-ion battery fast charging, we show that the learning approach not only ensures safe operation but also maximizes closed-loop performance. This includes maintaining the battery's operation below its maximum terminal voltage and reducing charging times, all achieved using a standard nominal MPC model with a short horizon and notable initial model-plant mismatch.

eess.SY↗
arXiv2024

Cycle Life Prediction for Lithium-ion Batteries: Machine Learning and More

Batteries are dynamic systems with complicated nonlinear aging, highly dependent on cell design, chemistry, manufacturing, and operational conditions. Prediction of battery cycle life and estimation of aging states is important to accelerate battery R&D, testing, and to further the understanding of how batteries degrade. Beyond testing, battery management systems rely on real-time models and onboard diagnostics and prognostics for safe operation. Estimating the state of health and remaining useful life of a battery is important to optimize performance and use resources optimally. This tutorial begins with an overview of first-principles, machine learning, and hybrid battery models. Then, a typical pipeline for the development of interpretable machine learning models is explained and showcased for cycle life prediction from laboratory testing data. We highlight the challenges of machine learning models, motivating the incorporation of physics in hybrid modeling approaches, which are needed to decipher the aging trajectory of batteries but require more data and further work on the physics of battery degradation. The tutorial closes with a discussion on generalization and further research directions.

eess.SY↗
arXiv2024

A direct optimization algorithm for input-constrained MPC

Providing an execution time certificate is a pressing requirement when deploying Model Predictive Control (MPC) in real-time embedded systems such as microcontrollers. Real-time MPC requires that its worst-case (maximum) execution time must be theoretically guaranteed to be smaller than the sampling time in closed-loop. This technical note considers input-constrained MPC problems and exploits the structure of the resulting box-constrained QPs. Then, we propose a \textit{cost-free} and \textit{data-independent} initialization strategy, which enables us, for the first time, to remove the initialization assumption of feasible full-Newton interior-point algorithms. We prove that the number of iterations of our proposed algorithm is \textit{only dimension-dependent} (\textit{data-independent}), \textit{simple-calculated}, and \textit{exact} (not \textit{worst-case}) with the value $\left\lceil\frac{\log(\frac{2n}ε)}{-2\log(\frac{\sqrt{2n}}{\sqrt{2n}+\sqrt{2}-1})}\right\rceil \!+ 1$, where $n$ denotes the problem dimension and $ε$ denotes the constant stopping tolerance. These features enable our algorithm to trivially certify the execution time of nonlinear MPC (via online linearized schemes) or adaptive MPC problems. The execution-time-certified capability of our algorithm is theoretically and numerically validated through an open-loop unstable AFTI-16 example.

math.OC↗
arXiv2024

Time-certified Input-constrained NMPC via Koopman Operator

Determining solving-time certificates of nonlinear model predictive control (NMPC) implementations is a pressing requirement when deploying NMPC in production environments. Such a certificate guarantees that the NMPC controller returns a solution before the next sampling time. However, NMPC formulations produce nonlinear programs (NLPs) for which it is very difficult to derive their solving-time certificates. Our previous work, Wu and Braatz (2023), challenged this limitation with a proposed input-constrained MPC algorithm having exact iteration complexity but was restricted to linear MPC formulations. This work extends the algorithm to solve input-constrained NMPC problems, by using the Koopman operator and a condensing MPC technique. We illustrate the algorithm performance on a high-dimensional, nonlinear partial differential equation (PDE) control case study, in which we theoretically and numerically certify the solving time to be less than the sampling time.

math.OC↗
arXiv2024

An Execution-time-certified Riccati-based IPM Algorithm for RTI-based Input-constrained NMPC

Establishing an execution time certificate in deploying model predictive control (MPC) is a pressing and challenging requirement. As nonlinear MPC (NMPC) results in nonlinear programs, differing from quadratic programs encountered in linear MPC, deriving an execution time certificate for NMPC seems an impossible task. Our prior work \cite{wu2023direct} introduced an input-constrained MPC algorithm with the exact and only \textit{dimension-dependent} (\textit{data-independent}) number of floating-point operations ([flops]). This paper extends it to input-constrained NMPC problems via the real-time iteration (RTI) scheme, which results in \textit{data-varying} (but \textit{dimension-invariant}) input-constrained MPC problems. Therefore, applying our previous algorithm can certify the execution time based on the assumption that processors perform fixed [flops] in constant time. As the RTI-based scheme generally results in MPC with a long prediction horizon, this paper employs the efficient factorized Riccati recursion, whose computational cost scales linearly with the prediction horizon, to solve the Newton system at each iteration. The execution-time certified capability of the algorithm is theoretically and numerically validated through a case study involving nonlinear control of the chaotic Lorenz system.

eess.SY↗
arXiv2024

Physics-based Modeling of Pulse and Relaxation of High-rate Li/CF$_{x}$-SVO batteries in Implantable Medical Devices

We present a physics-based model that accurately predicts the performance of Medtronic's implantable medical device battery lithium/carbon monofluoride (CF$_x$) - silver vanadium oxide (SVO) under both low-rate background monitoring and high-rate pulsing currents. The distinct properties of multiple active materials are reflected by parameterizing their thermodynamics, kinetics, and mass transport properties separately. Diffusion limitations of Li$^+$ in SVO are used to explain cell voltage transient behavior during pulse and post-pulse relaxation. We also introduce change in cathode electronic conductivity, Li metal anode surface morphology, and film resistance buildup to capture evolution of cell internal resistance throughout multi-year electrical tests. We share our insights on how the Li$^+$ redistribution process between active materials can restore pulse capability of the hybrid electrode, allow CF$_x$ to indirectly contribute to capacity release during pulsing, and affect the operation protocols and design principles of batteries with other hybrid electrodes. We also discuss additional complexities in porous electrode model parameterization and electrochemical characterization techniques due to parallel reactions and solid diffusion pathways across active materials. We hope our models implemented in the Hybrid Multiphase Porous Electrode Theory (Hybrid-MPET) framework can complement future experimental research and accelerate development of multi-active material electrodes with targeted performance.

cond-mat.mtrl-sci↗
arXiv2023

Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used differential equation solver library in a high-level language (Julia's DifferentialEquations.jl) and enables GPU acceleration without requiring code changes by the user. Our approach achieves state-of-the-art performance compared to hand-optimized CUDA-C++ kernels while performing 20--100$\times$ faster than the vectorizing map (vmap) approach implemented in JAX and PyTorch. Performance evaluation on NVIDIA, AMD, Intel, and Apple GPUs demonstrates performance portability and vendor-agnosticism. We show composability with MPI to enable distributed multi-GPU workflows. The implemented solvers are fully featured -- supporting event handling, automatic differentiation, and incorporation of datasets via the GPU's texture memory -- allowing scientists to take advantage of GPU acceleration on all major current architectures without changing their model code and without loss of performance. We distribute the software as an open-source library https://github.com/SciML/DiffEqGPU.jl

cs.DC↗
arXiv2023

Interpretation of High-Dimensional Linear Regression: Effects of Nullspace and Regularization Demonstrated on Battery Data

High-dimensional linear regression is important in many scientific fields. This article considers discrete measured data of underlying smooth latent processes, as is often obtained from chemical or biological systems. Interpretation in high dimensions is challenging because the nullspace and its interplay with regularization shapes regression coefficients. The data's nullspace contains all coefficients that satisfy $\mathbf{Xw}=\mathbf{0}$, thus allowing very different coefficients to yield identical predictions. We developed an optimization formulation to compare regression coefficients and coefficients obtained by physical engineering knowledge to understand which part of the coefficient differences are close to the nullspace. This nullspace method is tested on a synthetic example and lithium-ion battery data. The case studies show that regularization and z-scoring are design choices that, if chosen corresponding to prior physical knowledge, lead to interpretable regression results. Otherwise, the combination of the nullspace and regularization hinders interpretability and can make it impossible to obtain regression coefficients close to the true coefficients when there is a true underlying linear model. Furthermore, we demonstrate that regression methods that do not produce coefficients orthogonal to the nullspace, such as fused lasso, can improve interpretability. In conclusion, the insights gained from the nullspace perspective help to make informed design choices for building regression models on high-dimensional data and reasoning about potential underlying linear models, which are important for system optimization and improving scientific understanding.

stat.ML↗