We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy measurements of its mechanical response to loading. Conditional score-based diffusion models are generative models that learn to approximate the score function of a conditional distribution using samples from the joint distribution. More specifically, the score functions corresponding to multiple realizations of the measurement are approximated using a single neural network, the so-called score network, which is subsequently used to sample the posterior distribution using an appropriate Markov chain Monte Carlo scheme based on Langevin dynamics. Training the score network only requires simulating the forward model. Hence, the proposed approach can accommodate black-box forward models and complex measurement noise. Moreover, once the score network has been trained, it can be re-used to solve the inverse problem for different realizations of the measurements. We demonstrate the efficacy of the proposed approach on a suite of high-dimensional inverse problems in mechanics that involve inferring heterogeneous material properties from noisy measurements. Some examples we consider involve synthetic data, while others include data collected from actual elastography experiments. Further, our applications demonstrate that the proposed approach can handle different measurement modalities, complex patterns in the inferred quantities, non-Gaussian and non-additive noise models, and nonlinear black-box forward models. The results show that the proposed framework can solve large-scale physics-based inverse problems efficiently.

Prediction bias in machine learning models refers to unintended model behaviors that discriminate against inputs mentioning or produced by certain groups; for example, hate speech classifiers predict more false positives for neutral text mentioning specific social groups. Mitigating bias for each task or domain is inefficient, as it requires repetitive model training, data annotation (e.g., demographic information), and evaluation. In pursuit of a more accessible solution, we propose the Upstream Bias Mitigation for Downstream Fine-Tuning (UBM) framework, which mitigate one or multiple bias factors in downstream classifiers by transfer learning from an upstream model. In the upstream bias mitigation stage, explanation regularization and adversarial training are applied to mitigate multiple bias factors. In the downstream fine-tuning stage, the classifier layer of the model is re-initialized, and the entire model is fine-tuned to downstream tasks in potentially novel domains without any further bias mitigation. We expect downstream classifiers to be less biased by transfer learning from de-biased upstream models. We conduct extensive experiments varying the similarity between the source and target data, as well as varying the number of dimensions of bias (e.g., discrimination against specific social groups or dialects). Our results indicate the proposed UBM framework can effectively reduce bias in downstream classifiers.