Generalizing synthetic data-trained acoustic predictive models to real-world measurements

Acoustic Resonance Spectroscopy (ARS) is highly sensitive to structural properties such as material, geometry, and environmental conditions; as a consequence, it can noninvasively measure internal properties that are unobservable by most other methods. Because of its sensing capabilities and low implementation cost and complexity, ARS has potential as a paradigm shift in noninvasive sensing, characterization, and monitoring applications. However, extracting specific properties from ARS measurements, comprising the vibration spectrum of a test object, is challenging due to the sensitivity of the spectra to other structural changes not being measured, e.g., manufacturing tolerances, component coupling, environmental variation, etc. Neural Networks are promising tools for identifying trends in ARS measurements, but their training typically requires large datasets, which are often impractical to obtain for real-world systems. Synthetic data can be simulated efficiently, but discrepancies between synthetic and real-world data frequently lead to poor generalization when testing on the real-world data. We propose a novel ARS model training framework that enables developing a network that generalizes to predictions on real-world ARS measurements, but requires no labeled real-world data for training, instead relying on labeled synthetic data and the unlabeled real-world ARS measurements. Our approach leverages the Correlation Alignment (CORAL) technique to enforce the extraction of features common to both synthetic and real-world domains. As a case study, we demonstrate noninvasive ARS-based pressure measurements in sealed systems. Finite element method (FEM) simulations were used to generate synthetic training data across diverse vessel configurations and pressure conditions, and model performance was then tested on real-world measurements. We demonstrate that robust machine learning models for ARS can be developed without large real-world datasets, significantly broadening the applicability of ARS for noninvasive sensing. Moreover, the approach is extensible to other sensing modalities where synthetic data are abundant but real-world data are limited.

Acoustic Resonance Spectroscopy (ARS) methods have emerged as powerful noninvasive technique for estimating a variety of structural, material, and environmental properties by analyzing the vibrational resonance frequencies of a structure (Migliori and Sarrao, 1997; Leisure and Willis, 1997; Sinha, 1998; Davis et al., 2016; Greenhall et al., 2023a; Prisbrey et al., 2024; Pereira et al., 2025). Additionally, this resonance behavior enables acoustic resonance-based measurements in many sensing applications where no other noninvasive, nondestructive sensing methods exist. These include noninvasive, nondestructive detection and classification of chemical weapons (Sinha et al., 1995) and noninvasive, nondestructive measurement of full elasticity tensors (Migliori and Sarrao, 1997; Remillieux et al., 2015; Balakirev et al., 2019), residual stress (Kube et al., 2021; Ley et al., 2025), calibration-free internal pressure (Prisbrey et al., 2024; Pereira et al., 2025), and mechanical wear of embedded components (Greenhall et al., 2023a), to name a few.

The strength of ARS is attributed to the sensitivity of the system resonances to a wide range of properties. However, this also presents the primary challenge of ARS, which is attributing specific features in the acoustic resonance spectra (e.g., peak position, magnitude, skew, etc.) to the desired property to be measured, as opposed to the “undesired” properties, where the effects of the desired and undesired properties are highly coupled. As a result, variation in the undesired properties result in perturbations to the acoustic resonance spectra in the form of peaks shifting, deforming, merging, splitting, or being created or suppressed. These perturbations pose challenges for many chemometric signal processing methods designed for EM spectra, which have relatively simple spectral noise and trends found in electromagnetic (EM) spectroscopy like near-infrared (Geladi et al., 1985; Rinnan et al., 2009).

Recent advances in deep learning have shown promise in addressing these challenges. Deep Convolutional Neural Networks (CNNs) are well-suited for extracting meaningful features from complex signals like electromagnetic (EM) (Lee et al., 2020; Schuetzke et al., 2023) or acoustic spectra (Pereira et al., 2025). However, one of the main obstacles in training deep learning models is the lack of real-world labeled data in sufficient quantities to avoid overfitting so that the models can generalize to new data. Efforts have been made to create universal synthetic EM spectroscopy datasets to alleviate the burden of collecting experimental training measurements (Schuetzke et al., 2023). However, a universal synthetic dataset is infeasible for ARS measurements due to the high degree of variability in acoustic resonance spectra between different applications. Because of this, a new training dataset typically needs to be created when developing an ARS sensing method for a new, unique application or system. One solution to alleviate this issue is to use simulation to generate synthetic data, which can produce large quantities of training data relatively quickly and for low cost. However, any differences in physical assumptions, material properties, geometry, boundary conditions, etc., can lead to significant differences between the synthetic and real-world spectra, i.e., a domain gap. Because of this, complex models trained on synthetic data learn latent features that represent the synthetic data well but may not generalize to real-world data. As a result, these models may fail to accurately predict properties from real-world spectra due to differences in noise, signal distortions, and environmental variations.

To bridge the domain gap between synthetic and real-world data, unsupervised domain adaptation techniques have been developed to enable models to adapt using only unlabeled target samples (Tzeng et al., 2017; Radhakrishnan and Jay Kuo, 2018; Farahani et al., 2020; Zhong and Dietzen, 2025; Sun and Saenko, 2016; Sun et al., 2017). Generative Adversarial Networks (GANs) have been used to transform synthetic images into latent features that are “similar” to real-world latent features in the sense that a discriminator function cannot discern the difference between images from the two domains (Radhakrishnan and Jay Kuo, 2018). Methods such as Adversarial Discriminative Domain Adaptation (ADDA) aim to train a feature encoder on labeled synthetic data while adapting it to the real domain through an adversarial learning objective (Tzeng et al., 2017). While these adversarial methods can effectively reduce domain shift between source and target domains, they often suffer from vanishing gradients and sensitivity to initial weights and hyperparameters, which can cause instability or inconsistent model performance (Xing et al., 2017). A more comprehensive and robust unsupervised approach is offered by Correlation Alignment (CORAL) methods, where models are trained to learn domain-invariant representations by explicitly aligning the mean and covariance of latent features between synthetic and real-world domains (Sun et al., 2017). This results in a smooth objective function instead of an adversarial discriminator, which is less sensitivity to initial conditions and hyperparameters. This makes CORAL particularly appealing for ARS applications, where there is significant variation in the real-world data and a wide range of spectral behaviors in different sensing applications. These domain adaptation methods were initially developed for image processing and have expanded to other sensing modalities. However, to date, domain adaptation has not been implemented for ARS measurements, which have unique signal behavior and sensitivity to internal and external geometry, material(s), and environmental conditions that a structure is subject to.

In this manuscript we implement, for the first time, CORAL domain adaptation to enable training a CNN-based ARS model on labeled synthetic data that generalizes to real-world data. This CORAL training method would remove the primary barrier for development of an ARS sensing method - the need for large quantities of real-world training data. As a result, this work could result in wide adoption of ARS for a broad range of NDE applications requiring inexpensive, flexible, noninvasive measurement of unique structural, material, and/or environmental properties. Additionally, our findings have broader implications for other noninvasive testing methods where collecting real-world data is expensive or impractical, including structural health monitoring, material characterization, and various forms of non-destructive evaluation (NDE).

To demonstrate this new ARS training methodology, we apply the technique to measurement of internal pressure within sealed vessels. To date, ARS is the only method that enables noninvasive measurement of internal pressure without sensor calibration, i.e., attaching sensors at a known pressure then monitoring for changes (Prisbrey et al., 2024; Pereira et al., 2025). These models have been trained on labeled real-world data, which allows them to generalize to other real-world data for similar systems. In contrast, this work focuses on predicting the pressures in real-world vessels using a CNN model trained on labeled synthetic data with CORAL and compare the performance to the same CNN model using traditional training (without CORAL). Additionally, we demonstrate how to evaluate key CORAL training hyperparameters when developing new ARS sensing methods. These include the synthetic dataset size (number of simulations) and the dataset variation (range of simulation parameter values) necessary to train a model on synthetic data such that it generalizes to real-world data.

CORAL domain adaptation framework

To address the domain shift between synthetic and real-world ARS data, we consider latent-feature representations of the ARS spectra, which are computed by transforming the spectra via a model with trainable parameters. Here, we use a CNN based on prior performance with ARS measurements (Pereira et al., 2025). We then perform unsupervised domain adaptation using a CORAL architecture adapted from (Sun et al., 2017). Figure 1 illustrates the CORAL concept for aligning two datasets with different domains: synthetic (blue) and real-world (orange). CORAL drives the initially unaligned distributions together by attempting to minimize the differences between the synthetic and real-world feature covariances, while simultaneously minimizing label prediction error for the synthetic samples. This process encourages the model to learn domain-invariant model parameters, thereby improving generalization to unseen experimental conditions. This approach allows us to transfer knowledge learned from labeled synthetic data to unlabeled real-world data by aligning feature distributions in a domain-invariant latent space.

The domain adaptation framework includes two trainable networks: a shared feature extractor and a label regressor to predict pressure, as illustrated in Figure 2. The feature extractor maps input both synthetic (x s) and real-world (x r) spectra into a common latent feature space (See Section 2.1. for feature extractor details). The regressor then predicts the synthetic pressure labels (y ^ s). The goal of the model training is twofold: first to improve predictions on labeled synthetic data by reducing a label loss function (L l a b), and second to align the synthetic and real-world data by reducing a CORAL loss function (L C O R A L). Here, we use the Mean Squared-Error (MSE) as our label loss shown in Equation 1, where · is the L 2 -Norm, and the bold y s and y ^ s refer to the vectors of all synthetic labels and predicted labels. Additionally, we use the Frobenius norm as the CORAL loss (Sun and Saenko, 2016) shown in Equation 2, where C s and C r are the synthetic and real-world domain covariance matrices, respectively, for one training batch. The alignment process does not require labeled real-world data and is implemented by the following objective function shown in Equation 3: where the Lagrange multiplier, λ is a tunable hyperparameter that controls how much the optimization prioritizes minimizing the predicted synthetic label error versus minimizing the domain difference between the synthetic and real-world latent feature distributions.

We utilize an Adaptive Momentum (ADAM) optimizer to iteratively update all network parameters to minimize the total loss, resulting in a model that performs well on both synthetic and real-world data. The model was trained using both synthetic and experimental datasets to enable domain adaptation through CORAL. The available labeled synthetic data was divided into training (80%) and validation (20%) sets, and the real-world spectra were used both in training and testing, where the real-world labels were withheld from the model during training. During training, batches of training samples were constructed by sampling an equal number of synthetic and real-world examples, allowing both the regression and CORAL alignment losses to be computed per batch. The total loss L t o t a l ​ was minimized using the Adam optimizer with an initial learning rate of 7.5 × 10 −5. Early stopping based on the validation loss was applied to prevent overfitting. The weighting factor λ was empirically defined to balance prediction accuracy and feature alignment, ensuring stable convergence. All models were implemented in Python using Tensorflow 2.10 and trained on a workstation equipped with an NVIDIA RTX A6000 GPU.

Feature extractor architecture

The feature extractor consists of a Residual Network (ResNet) architecture, as shown in Figure 3, which was chosen for its ability to extract hierarchical and discriminative features from 1D signals and because it has been previously shown to successfully learn trends relating ARS measurements and internal pressure (Pereira et al., 2025; Ismail Fawaz et al., 2019). The input spectrum is passed through a series of three ResNet blocks. Each block comprises a series of four convolution (Conv1D) layers, each followed by a rectified linear unit (ReLU) activation and batch normalization (BN) layer. We used 240 kernels of lengths 69, 45, 28, and 10 in Conv1D layers one to four, respectively, of ResNet block 1; and 480 kernels of lengths 69, 45, 28, and 10 in Conv1D layers one to four, respectively, of ResNet blocks two and 3. Empirically, we observe that this relatively large network size is necessary to provide the flexibility to simultaneously learn synthetic features that correlate with the synthetic labels, while also providing distributions of synthetic and real-world latent features. Depending on the object being inspected, the network complexity and even architecture should be re-examined for new ARS sensing applications. The key to the ResNet block is a residual connection that bypasses all four Conv1D-ReLU-BN layers, which has been shown to mitigate the vanishing gradient problem, which improves gradient flow, accuracy, and convergence speed (Mahapatra et al., 2023). At the end of the network, a global average pooling (GAP) layer is applied, which computes the average value per channel of the final Conv1D layer, effectively reducing the output to a fixed-length vector that summarizes the most salient features. The GAP layer outputs a feature vector of size 480, which is then passed to both the label regressor and the domain discriminator during training.

Model performance metrics

Model performance was evaluated quantitatively using both label accuracy and domain alignment criteria. The primary metric for label accuracy was the root mean square error (RMSE) between the true y and predicted labels y ^ for the real-world dataset. In addition, the coefficient of determination (R 2) was computed to assess the proportion of variance in the measured data explained by the model predictions. To evaluate domain adaptation performance, the alignment between the synthetic and experimental feature distributions was visualized using t-distributed stochastic neighbor embedding (t-SNE) projections. Qualitatively, better alignment is reflected by overlapping distributions of synthetic and real-world latent space embeddings in the t-SNE space. Quantitatively, improvements in domain generalization were inferred from reductions in RMSE and increased consistency across both domains. Together, these metrics provide complementary insights into the model’s predictive accuracy and its capacity to learn domain-invariant representations through CORAL alignment.

Datasets

Real-world data

We collected real-world ARS measurements on a pressure vessel using the setup shown in Figure 4A. A stainless-steel vessel with approximate outer diameter D = 185 mm, height H = 222 mm, and wall thickness w = 0.80 mm, covered by a polymethyl methacrylate (PMMA) lid was used as a test system. The pressure was lowered using a vacuum pump and increased up to atmospheric using a pressure release valve, while the “true” internal pressure is measured via a capacitance manometer (MKS Baratron type 626). Two piezoelectric transducers, one emitter and one receiver (PZT-5J, 15 mm diameter, 1.7 MHz thickness mode, STEMiNC) were attached to the outer wall of the vessel with a vertical separation of approximately 100 mm via cyanoacrylate (Loctite ultragel control). We collected ARS measurements from 0.5 kHz–1.5 kHz using a vector network analyzer (VNA, Omicron Labs Bode100) and a 60 dB preamp (Olympus 566B). For each vessel, we performed four identical pressure step experiments. Each experiment consisted of adjusting the internal pressure from 25 Torr–575 Torr in 25 Torr steps, where ARS measurements were performed at each step. Additionally, we removed and replaced the transducers to replicate variability in transducer coupling. A total of 92 real-world labeled spectra were obtained.

To improve the signal quality and enhance subtle spectral features, we applied a four-step preprocessing pipeline consisting of smoothing, amplitude normalization, logarithmic scaling, and down-sampling. This procedure was designed to reduce noise, compensate for variations in resonance amplitudes, and produce spectra that are more comparable across measurements. A detailed mathematical description of the preprocessing steps can be found in Greenhall et al. (Greenhall et al., 2023b).

Synthetic data

To generate synthetic training data, we simulated the system described in Section 2.4. a using COMSOL 6.2 (see Figure 4B). Shell physics were used to simulate the vibrational modes in the vessel walls with reduced computational complexity, compared to simulating the full solid mechanics. We define the geometry based on experimental measurements of the vessel (115 mm diameter, 220 mm height, and 0.81 mm thickness) and lid (202 mm diameter and 11 mm thickness). Here, we are assuming perfect axial symmetry for both components. For the cylindrical vessel walls used COMSOL’s default material properties for 304 stainless, which include Young’s modulus 208.2 GPa, Poisson ratio 0.28, and density 7,931.1 kg/m 3. For the lid, we used COMSOL’s default material properties for Poly (methyl methacrylate) (PMMA), which include Young’s modulus 3.2 GPa, Poisson ratio 0.35, and density 1,190.0 kg/m 3. We modeled the acoustic emitter using sinusoidal out-of-plane point force applied on the side of the vessel. The receiver was modeled by a point probe measuring the out-of-plane displacement 100 mm apart from the emitter, which assumes that the measured displacement has little variance over the approximately 1 mm diameter transducer contact. A tetrahedral element with a maximum mesh size of 0.5 mm was used to discretize the shell surface. We simulated internal vacuum by applying a static pressure difference boundary condition across the vessel wall. We constrained the vessel via a fixed boundary condition at the container bottom to represent table. A two-step study was used to first apply the static pressure to deform the vessel and then perform a frequency sweep study to simulate the ARS measurement. The simulations were run for a range of internal pressures, p, varying between 25–575 Torr, in steps of 25 torr, to mimic the real-world measurements.

Figure 4C shows a comparison between the simulated (blue) and experimental spectra (orange) at an internal pressure of p = 150 Torr. We observe similar numbers of peaks with similar spacing. However, there are clear differences between the absolute peak positions and the peak widths and heights. This indicates that, after using a CNN to extract features, there will be a domain gap between the simulated and real-world data.

To increase the variability in the synthetic data, we repeated the pressure experiment simulations, where we perturbed several key simulation parameters, including the container height H, outer diameter D, and wall thickness w. In each pressure experiment, the values were selected from normal distributions θ n ∼ N μ n, σ n 2, where μ n is the mean and σ n is the standard deviation for each parameter n ∈ H, H / D, w. We assigned the measured parameters to the values of μ n. We hypothesized that the standard deviation would affect performance. To test this hypothesis, we characterize performance in terms of an overall standard deviation magnitude, given as shown in Equation 4, where we account for differences in parameter scale by using normalized standard deviations σ ∼ n = σ n / Ω n. Here, Ω n scales the effects of different parameters on the spectrum. To achieve this, we measured the average frequency shift of the experimental peaks due to a 25 Torr change in pressure (300 Torr–325 Torr), which we used to calculate the real-world peak shift Δ f t a r g e t. Next, for each parameter, we simulated ranges of the parameter value u n = μ n ± Δ u n (using nominal values μ n ′ for all other parameters n ′ ≠ n, and half-atmospheric pressure) and assigned the parameter scale Ω n to be the parameter shift Δ u n that resulted in an average peak shift of Δ f = Δ f t a r g e t. Here, the use of Δ f t a r g e t as the real-world shift is arbitrary. So long as Δ f t a r g e t is selected within a range where Δ f is approximately linear with respect to p (or any other property to be measured), then larger pressures simply result in larger, but approximately proportionate parameter scales Ω n. The values of Ω n for each of the perturbed parameters are shown in Table 1.

Model evaluation on unseen real-world data

To illustrate the benefits of domain alignment, we train our model on labeled data from simulations and unlabeled experimental data using the CORAL domain alignment and then test the prediction accuracy on the test data and compare the results to those achieved from the same model, trained traditionally, i.e., minimize the label error for the training data. Figure 5A shows a parity plot of the predicted pressure versus the true pressure for the test samples using training with traditional training (orange) and CORAL domain alignment (blue). Additionally, Figures 5B,C shows t-Distributed Stochastic Neighbor Embeddings (TSNE) of the latent features extracted using (B) training with CORAL domain alignment and (C) traditional training. We observe substantially lower prediction errors and higher coefficient of determination (r 2) values for CORAL training (RMSE = 48.5 Torr, r 2 = 0.92), compared to traditional training (RMSE = 179.8 Torr, r 2 = −0.12). These statistics indicate that CORAL training results in a model that generalizes well to the real-world data and predict pressure (or other property of interest) with a high degree of accuracy, in contrast to traditional training, which leads to model overfitting.

The TSNE embeddings further reveal that CORAL leads to a more coherent and aligned feature distribution between synthetic and real-world data domains, suggesting that the alignment procedure effectively mitigates discrepancies in feature representations. Overall, these results confirm that CORAL substantially enhances generalization from synthetic data to real-world measurements, which demonstrates the potential for replacing the need to collect vast amounts of experimental training data with relatively rapid, inexpensive synthetic training data. This has significant implications for ARS measurement applications, which have demonstrated unique sensing capabilities and high sensitivity, but have been limited by the large quantities of experimental data required for training. In subsequent sections, we explore how ARS with CORAL domain alignment is affected by key parameters, including CORAL Lagrangian factor λ and the size and distribution of the synthetic training dataset, which will help guide development of future ARS sensing applications.

Influence of CORAL Lagrangian factor

The CORAL Lagrangian factor λ dictates how strongly alignment should be enforced, versus how strongly the predicted training label error should be minimized. We trained the model using values of λ ranging from 0 (no domain alignment) to 0.4 (more weight given to domain alignment), where for each λ value, we repeated the training process 10 times. Here, we fixed the size of the source dataset to 2,408 samples and the synthetic dataset distribution amplitude to σ ∼ = 0.1.

Figure 6 shows the test pressure prediction RMSE as a function of λ, where the error bars represent the standard deviation in RMSE over the repeated trainings. For λ = 0, we observe large values for the RMSE mean and standard deviation, due to the lack of any adaptation between the synthetic and real-world domains. In this case, there are some instances where the trained model generalizes well to real-world data based on the specific initialized model parameters and training/validation data arrangement. However, the likelihood of achieving that generalizable trained model is low. As λ increases, we see an immediate drop in the RMSE standard deviation, which indicates that any domain adaptation yields more consistent model training. We observe that increasing λ reduces the mean RMSE until λ ≥ 0.25, after which the mean RMSE approximately asymptotes to values around 50 Torr. We empirically set λ = 0.25 for subsequent investigations in this manuscript. It is likely that changes in the ARS sensing application such as different structures, properties of interest, etc., would necessitate recreating the RMSE versus λ curve to identify the optimal λ value.

Effect of training dataset size

When developing an ARS-based sensing method for a new application, there is always a question about how much data is required to train your model. To answer this question, we generate progressively larger synthetic datasets with fixed parameter distributions σ ∼ = 0.1, and monitor the resulting effect on RMSE for the real-world data, whose size remains fixed. For the CORAL training, we use a fixed Lagrange multiplier of λ = 0.25, which is where performance approximately asymptotes (See Figure 6). Figure 7 shows the real-world predicted pressure RMSE from the model trained using traditional training (orange) and training with CORAL domain adaptation (blue). For each training dataset size, we repeated the training/testing procedure 10 times and calculated the mean (dots) and standard deviations (lines) in RMSE.

For the traditional training, we observe that increasing dataset sizes result in increasing mean RMSE with approximately constant variance. This is likely because increasing the synthetic dataset size will fill out the latent feature distribution. This allows for the model to better represent the synthetic data at the cost of reduced generalization to the real-world data due to the inherent domain gap between the synthetic and real-world data. Alternatively, for the CORAL training, we observe that increasing synthetic dataset size reduces the RMSE mean and variance. The significant drop in variance from dataset sizes of 100–120 indicates that >100 synthetic samples is sufficient for our pressure sensing application, while >600 samples results in the lowest mean RMSE. For future ARS applications, this process will need to be followed again to identify a sufficiently large synthetic dataset.

Effect of dataset distribution

When developing an ARS-based sensing method for a new application, simulation parameters must be selected to generate the synthetic data for training. The nominal parameters can typically be acquired by looking up typical material properties and measuring the dimensions of the system of interest. However, there will inevitably be differences between the simulated system and the real-world system, which will result in a domain gap between the synthetic and real-world latent features. This gap can also vary when considering application to multiple real-world systems of the same make/model, e.g., if manufacturing tolerances are large. Thus, it is desirable to include variation in the simulation parameters to enable the model to learn features in the synthetic data that correspond to the property of interest, despite differences between the simulated and real-world systems. The remaining question is how much parameter variation to use. We apply different dataset distribution amplitudes ranging from σ ∼ = 0 to 4.0 and measure the effect on RMSE. For each distribution, we draw 2,408 samples; and for all CORAL training, we use a fixed Lagrange multiplier of λ = 0.25. Similar to the other studies, we repeat each train/test procedure 10 times and record the real-world predicted pressure RMSE for each training.

Figure 8 shows the RMSE as a function of the normalized synthetic dataset distribution amplitude for models trained traditionally (orange) and using CORAL domain alignment (blue). For the traditional training, we observe that the RMSE remains approximately constant for distributions σ ∼ < 0.03, but that subsequent increases in σ ∼ lead to large increases in RMSE. This is likely due to the fact that increasing σ ∼ will broaden the latent feature distribution n, while the distribution of real-world samples does not change accordingly. Thus, the average distance between any given pair of real-world and synthetic samples increases in the latent feature space, resulting in reduced generalizability. In contrast, the CORAL training forces latent feature distributions closer to one another, which results in the model identifying the features corresponding to pressure in the presence of noise in other parameters. This results in much lower RMSE mean and variance, and less sensitivity of the RMSE to the simulation parameter distribution, as shown in Figure 8. We do observe that the CORAL RMSE increases slightly for σ ∼ > 0.2. This indicates that there is an optimal parameter distribution that should be identified to maximize performance of the ARS sensing method. However, we still find that the CORAL domain alignment increases model accuracy and robustness significantly, compared to traditional training.

In this manuscript, we empirically selected three parameters to insert the variability to achieve generalizability. It is currently unknown if there is a minimum required number or combination of parameters for a given application. In practice, for new ARS sensing method developments, the developer will need to identify the sufficient combination of parameters to vary. Thus, to develop the new method, we recommend identifying as many candidate parameters as possible, and then determining the correct number of parameters by applying variance in one parameter at a time until the CORAL trained model demonstrates sufficient generalizability, i.e., treat the parameter selection as a tunable hyperparameter.

While the present work focuses on the application of measuring pressure in sealed vessels, the CORAL training method can theoretically be extended to measuring a wide variety of structural, material, or environmental properties, as long as the ARS measurements are sufficiently sensitive to that property. The same process described in this manuscript can be applied to these measurements, i.e., create a baseline numerical simulation, identify key physical properties to perturb, create a synthetic dataset where the measured property is simulated over the range of expected real-world values and the other key properties are varied randomly, and then perform CORAL training with the labeled synthetic data and unlabeled real-world measurements. Here, it is suggested that the dataset distribution, dataset size, and Lagrangian factor are tuned as they were in this work.

Conclusion

We present a method for generalizing ARS sensing models trained on synthetic labeled data to unlabeled real-world data using CORAL. We demonstrate improved performance by training a neural network on synthetic acoustic resonance spectra simulated via the Finite Element Method and tested on real-world acoustic resonance spectra measured on a vacuum can with unknown internal pressures. We find that the CORAL training method provides improvements on the order of 73% reduction in RMSE and a 1.04 increase in the r 2 coefficient, compared to traditional training. Additionally, we show the robustness of the CORAL training method to variation in training dataset size and parameter distribution. As a result, we demonstrate, for the first time, a method of training a neural network model on synthetic data that can be generalized to real-world data. This ability has significant implications for ARS sensing; which is inexpensive, noninvasive, nondestructive, and is sensitive to properties not accessible to traditional sensing methods; but is currently limited by the large volumes of experimental data required to train the models. By replacing the experimental data, which is expensive and time-intensive to collect, with simulated data that can be created rapidly and in large quantities, we remove the primary bottleneck prohibiting wide-use of ARS. While further work is required to determine how well the method extends to other applications, our example application measuring pressure in a sealed vessel demonstrates the feasibility of training an ARS model without labeled real-world data. This has significant implications for the NDE applications such as manufacturing quality assurance, structural health monitoring, biomedical diagnostics, and national security; where ARS could provide inexpensive, noninvasive, highly sensitive measurement of a wide range of material, structural, and environmental properties. Additionally, the CORAL training method can be extended to other sensor technologies where experimental training data is sparse and simulation data on its own does not have sufficient fidelity.