Digital twins in mechanical and aerospace engineering.

Digital twins bring value to mechanical and aerospace systems by speeding up development, reducing risk, predicting issues and reducing sustainment costs. Realizing these benefits at scale requires a structured and intentional approach to digital twin conception, design, development, operation and sustainment. To bring maximal value, a digital twin does not need to be an exquisite virtual replica but instead must be envisioned to be fit for purpose, where the determination of fitness depends on the capability needs and the cost-benefit trade-offs.

Learning physics-based reduced-order models from data using nonlinear manifolds.

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

Predictive digital twin for optimizing patient-specific radiotherapy regimens under uncertainty in high-grade gliomas.

We develop a methodology to create data-driven predictive digital twins for optimal risk-aware clinical decision-making. We illustrate the methodology as an enabler for an anticipatory personalized treatment that accounts for uncertainties in the underlying tumor biology in high-grade gliomas, where heterogeneity in the response to standard-of-care (SOC) radiotherapy contributes to sub-optimal patient outcomes. The digital twin is initialized through prior distributions derived from population-level clinical data in the literature for a mechanistic model's parameters. Then the digital twin is personalized using Bayesian model calibration for assimilating patient-specific magnetic resonance imaging data. The calibrated digital twin is used to propose optimal radiotherapy treatment regimens by solving a multi-objective risk-based optimization under uncertainty problem. The solution leads to a suite of patient-specific optimal radiotherapy treatment regimens exhibiting varying levels of trade-off between the two competing clinical objectives: (i) maximizing tumor control (characterized by minimizing the risk of tumor volume growth) and (ii) minimizing the toxicity from radiotherapy. The proposed digital twin framework is illustrated by generating an in silico cohort of 100 patients with high-grade glioma growth and response properties typically observed in the literature. For the same total radiation dose as the SOC, the personalized treatment regimens lead to median increase in tumor time to progression of around six days. Alternatively, for the same level of tumor control as the SOC, the digital twin provides optimal treatment options that lead to a median reduction in radiation dose by 16.7% (10 Gy) compared to SOC total dose of 60 Gy. The range of optimal solutions also provide options with increased doses for patients with aggressive cancer, where SOC does not lead to sufficient tumor control.

Localized non-intrusive reduced-order modelling in the operator inference framework.

This paper presents data-driven learning of localized reduced models. Instead of a global reduced basis, the approach employs multiple local approximation subspaces. This localization permits adaptation of a reduced model to local dynamics, thereby keeping the reduced dimension small. This is particularly important for reduced models of nonlinear systems of partial differential equations, where the solution may be characterized by different physical regimes or exhibit high sensitivity to parameter variations. The contribution of this paper is a non-intrusive approach that learns the localized reduced model from snapshot data using operator inference. In the offline phase, the approach partitions the state space into subregions and solves a regression problem to determine localized reduced operators. During the online phase, a local basis is chosen adaptively based on the current system state. The non-intrusive nature of localized operator inference makes the method accessible, portable and applicable to a broad range of scientific problems, including those that use proprietary or legacy high-fidelity codes. We demonstrate the potential for achieving large computational speedups while maintaining good accuracy for a Burgers' equation governing shock propagation in a one-dimensional domain and a phase-field problem governed by the Cahn-Hilliard equation. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

Predictive Radiation Oncology - A New NCI-DOE Scientific Space and Community.

With a widely attended virtual kickoff event on January 29, 2021, the National Cancer Institute (NCI) and the Department of Energy (DOE) launched a series of 4 interactive, interdisciplinary workshops-and a final concluding "World Café" on March 29, 2021-focused on advancing computational approaches for predictive oncology in the clinical and research domains of radiation oncology. These events reflect 3,870 human hours of virtual engagement with representation from 8 DOE national laboratories and the Frederick National Laboratory for Cancer Research (FNL), 4 research institutes, 5 cancer centers, 17 medical schools and teaching hospitals, 5 companies, 5 federal agencies, 3 research centers, and 27 universities. Here we summarize the workshops by first describing the background for the workshops. Participants identified twelve key questions-and collaborative parallel ideas-as the focus of work going forward to advance the field. These were then used to define short-term and longer-term "Blue Sky" goals. In addition, the group determined key success factors for predictive oncology in the context of radiation oncology, if not the future of all of medicine. These are: cross-discipline collaboration, targeted talent development, development of mechanistic mathematical and computational models and tools, and access to high-quality multiscale data that bridges mechanisms to phenotype. The workshop participants reported feeling energized and highly motivated to pursue next steps together to address the unmet needs in radiation oncology specifically and in cancer research generally and that NCI and DOE project goals align at the convergence of radiation therapy and advanced computing.

Scaling digital twins from the artisanal to the industrial.

Mathematical modeling and simulation are moving from being powerful development and analysis tools towards having increased roles in operational monitoring, control and decision support, in which models of specific entities are continually updated in the form of a digital twin. However, current digital twins are largely the result of bespoke technical solutions that are difficult to scale. We discuss two exemplar applications that motivate challenges and opportunities for scaling digital twins, and that underscore potential barriers to wider adoption of this technology.

A probabilistic graphical model foundation for enabling predictive digital twins at scale.

A unifying mathematical formulation is needed to move from one-off digital twins built through custom implementations to robust digital twin implementations at scale. This work proposes a probabilistic graphical model as a formal mathematical representation of a digital twin and its associated physical asset. We create an abstraction of the asset-twin system as a set of coupled dynamical systems, evolving over time through their respective state spaces and interacting via observed data and control inputs. The formal definition of this coupled system as a probabilistic graphical model enables us to draw upon well-established theory and methods from Bayesian statistics, dynamical systems and control theory. The declarative and general nature of the proposed digital twin model make it rigorous yet flexible, enabling its application at scale in a diverse range of application areas. We demonstrate how the model is instantiated to enable a structural digital twin of an unmanned aerial vehicle (UAV). The digital twin is calibrated using experimental data from a physical UAV asset. Its use in dynamic decision-making is then illustrated in a synthetic example where the UAV undergoes an in-flight damage event and the digital twin is dynamically updated using sensor data. The graphical model foundation ensures that the digital twin calibration and updating process is principled, unified and able to scale to an entire fleet of digital twins.

Development of a computational model for astronaut reorientation.

The ability to model astronaut reorientations computationally provides a simple way to develop and study human motion control strategies. Since the cost of experimenting in microgravity is high, and underwater training can lead to motions inappropriate for microgravity, these techniques allow for motions to be developed and well-understood prior to any microgravity exposure. By including a model of the current space suit, we have the ability to study both intravehicular and extravehicular activities. We present several techniques for rotating about the axes of the body and show that motions performed by the legs create a greater net rotation than those performed by the arms. Adding a space suit to the motions was seen to increase the resistance torque and limit the available range of motion. While rotations about the body axes can be performed in the current space suit, the resulting motions generated a reduced rotation when compared to the unsuited configuration.

Kinetics and kinematics for translational motions in microgravity during parabolic flight.

INTRODUCTION: Astronauts soaring through space modules with the grace of birds seems counterintuitive. How do they adapt to the weightless environment? Previous spaceflights have shown that astronauts in orbit adapt their motor strategies to each change in their gravitational environment. During adaptation, performance is degraded and can lead to mission-threatening injuries. If adaptation can occur before a mission, productivity during the mission might improve, minimizing risk. The goal is to combine kinetic and kinematic data to examine translational motions during microgravity adaptations. METHODS: Experiments were performed during parabolic flights aboard NASA's C-9. Five subjects used their legs to push off from a sensor, landing on a target 3.96 m (13 ft) away. The sensor quantified the kinetics during contact, while four cameras recorded kinematics during push-off. Joint torques were calculated for a subset of traverses (N = 50) using the forces, moments, and joint angles. RESULTS: During the 149 traverses, the average peak force exerted onto the sensor was 224.6 +/- 74.6 N, with peak values ranging between 65.8-461.9 N. Two types of force profiles were observed, some having single, strong peaks (N = 64) and others having multiple, weaker peaks (N = 86). CONCLUSIONS: The force data were consistent with values recorded previously in sustained microgravity aboard Mir and the Space Shuttle. A training program for astronauts might be designed to encourage fine-control motions (i.e., multiple, weaker peaks) as these reduce the risk of injury and increase controllability. Additionally, a kinematic and kinetic sensor suite was successfully demonstrated in the weightless environment onboard the C-9 aircraft.

Self-rotations in simulated microgravity: performance effects of strategy training.

INTRODUCTION: This research studies reorientation methodologies in a simulated microgravity environment using an experimental framework to reduce astronaut adaptation time and provide for a safety countermeasure during extravehicular activity. METHODS: There were 20 subjects (10 men, 10 women, mean age of 23.6 +/- 3.5) who were divided into 2 groups, fully trained and minimally trained, which determined the amount of motion strategy training received. Subjects performed a total of 48 rotations about their pitch, roll, and yaw axes in a suspension system that simulated microgravity. In each trial subjects either rotated 90 degrees in pitch, 90 degrees in roll, or 180 degrees in yaw. Experimental measures include subject coordination, performance time, cognitive workload assessments, and qualitative motion control strategies. RESULTS: Subjects in the fully trained group had better initial performance with respect to performance time and workload scores for the pitch and yaw rotations. Further, trained subjects reached a steady-state performance time in fewer trials than those with minimal training. The subjects with minimal training tended to use motions that were common in an Earth environment since no technique was provided. For roll rotations they developed motions that would have led to significant off-axis (pitch and yaw) rotations in a true microgravity environment. CONCLUSIONS: We have shown that certain body axes are easier to rotate about than others and that fully trained subjects had an easier time performing the body rotations than the minimally trained subjects. This study has provided the groundwork for the development of an astronaut motion-control training program.