Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling

Constitutive modeling under uncertainty remains a central challenge for reliable mechanics simulations, particularly when the available stress-deformation data are sparse, noisy, or heterogeneous. We propose interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) for uncertainty-aware hyperelastic constitutive modeling. iPANNs learn sparse lower, mean, and upper free energy density branches whose stresses, obtained by automatic differentiation, ultimately enclose noisy stress observations. In contrast to this deterministic interval description, fPANNs embed the learned iPANN branches into a fuzzy-set representation through alpha-cut interpolation, yielding a nested family of admissible responses. iPANNs and fPANNs encode mechanistic constraints - preserving objectivity, consistency and promoting polyconvexity - and smoothed L0 regularization promotes interpretable energy representations. The bound models are trained through a two-stage transfer-learning procedure in which a sparse mean constitutive response is learned first and then fine-tuned into lower and upper energy branches. We evaluate the framework on synthetic isotropic hyperelastic data with heteroscedastic noise, varying random realizations, shifted noise means, and varying noise magnitudes. The results show that the learned bounds enclose noisy stress observations while generalizing to the test set. Further, we examine the propagation of uncertainty through the mean, upper and lower bound predictions of the learned iPANN models in a finite element setting. The proposed framework provides a compact, physics-consistent route for distribution-free aleatoric uncertainty quantification in hyperelastic constitutive modeling, and propagation in downstream finite element simulations.

Towards end-to-end optimization in multimaterial 3D printing

Multimaterial 3D printing enables the fabrication of functionally graded components, but optimizing their spatial material distribution alongside structural topology remains a formidable challenge due to high-dimensional design spaces and complex constitutive modeling. This paper presents an end-to-end computational framework integrating sparsified physics-augmented neural networks with finite-element-based topology optimization. By extracting closed-form, composition-aware hyperelastic constitutive laws from experimental data, this approach facilitates exact symbolic differentiation via the adjoint state method implemented with FEniCSx, efficiently circumventing the bottlenecks of applying neural network constitutive models. This pipeline is deployed on soft robotic gripper applications, demonstrating continuous composition optimization for highly anisotropic contact responses, and the concurrent optimization of macroscopic topology and material distribution under non-failure stretch constraints. This methodology could replace laborious empirical prototyping, establishing interpretable machine-learning models as practical, robust design primitives for advanced multimaterial additive manufacturing.

Zero-Shot Metric Depth Estimation via Monocular Visual-Inertial Rescaling for Autonomous Aerial Navigation

This paper presents a methodology to predict metric depth from monocular RGB images and an inertial measurement unit (IMU). To enable collision avoidance during autonomous flight, prior works either leverage heavy sensors (e.g., LiDARs or stereo cameras) or data-intensive and domain-specific fine-tuning of monocular metric depth estimation methods. In contrast, we propose several lightweight zero-shot rescaling strategies to obtain metric depth from relative depth estimates via the sparse 3D feature map created using a visual-inertial navigation system. These strategies are compared for their accuracy in diverse simulation environments. The best performing approach, which leverages monotonic spline fitting, is deployed in the real-world on a compute-constrained quadrotor. We obtain on-board metric depth estimates at 15 Hz and demonstrate successful collision avoidance after integrating the proposed method with a motion primitives-based planner.

Distributional Advantage Actor-Critic

In traditional reinforcement learning, an agent maximizes the reward collected during its interaction with the environment by approximating the optimal policy through the estimation of value functions. Typically, given a state s and action a, the corresponding value is the expected discounted sum of rewards. The optimal action is then chosen to be the action a with the largest value estimated by value function. However, recent developments have shown both theoretical and experimental evidence of superior performance when value function is replaced with value distribution in context of deep Q learning [1]. In this paper, we develop a new algorithm that combines advantage actor-critic with value distribution estimated by quantile regression. We evaluated this new algorithm, termed Distributional Advantage Actor-Critic (DA2C or QR-A2C) on a variety of tasks, and observed it to achieve at least as good as baseline algorithms, and outperforming baseline in some tasks with smaller variance and increased stability.