Dong Heon Cho

Peter Yichen Chen, Jinxu Xiang, Dong Heon Cho et al.

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce the dimensionality of discretized vector fields, our continuous reduced-order modeling (CROM) approach builds a low-dimensional embedding of the continuous vector fields themselves, not their discretization. We represent this reduced manifold using continuously differentiable neural fields, which may train on any and all available numerical solutions of the continuous system, even when they are obtained using diverse methods or discretizations. We validate our approach on an extensive range of PDEs with training data from voxel grids, meshes, and point clouds. Compared to prior discretization-dependent ROM methods, such as linear subspace proper orthogonal decomposition (POD) and nonlinear manifold neural-network-based autoencoders, CROM features higher accuracy, lower memory consumption, dynamically adaptive resolutions, and applicability to any discretization. For equal latent space dimension, CROM exhibits 79$\times$ and 49$\times$ better accuracy, and 39$\times$ and 132$\times$ smaller memory footprint, than POD and autoencoder methods, respectively. Experiments demonstrate 109$\times$ and 89$\times$ wall-clock speedups over unreduced models on CPUs and GPUs, respectively. Videos and codes are available on the project page: https://crom-pde.github.io

Taeoh Kim, Hyeongmin Lee, MyeongAh Cho et al.

Deep-Learning-based video recognition has shown promising improvements along with the development of large-scale datasets and spatiotemporal network architectures. In image recognition, learning spatially invariant features is a key factor in improving recognition performance and robustness. Data augmentation based on visual inductive priors, such as cropping, flipping, rotating, or photometric jittering, is a representative approach to achieve these features. Recent state-of-the-art recognition solutions have relied on modern data augmentation strategies that exploit a mixture of augmentation operations. In this study, we extend these strategies to the temporal dimension for videos to learn temporally invariant or temporally localizable features to cover temporal perturbations or complex actions in videos. Based on our novel temporal data augmentation algorithms, video recognition performances are improved using only a limited amount of training data compared to the spatial-only data augmentation algorithms, including the 1st Visual Inductive Priors (VIPriors) for data-efficient action recognition challenge. Furthermore, learned features are temporally localizable that cannot be achieved using spatial augmentation algorithms. Our source code is available at https://github.com/taeoh-kim/temporal_data_augmentation.

Dong Heon Cho, Boyuan Chen

Differentiable simulators enable gradient-based optimization of soft robots over material parameters, control, and morphology, but accurately modeling real systems remains challenging due to the sim-to-real gap. This issue becomes more pronounced when geometry is itself a design variable. System identification reduces discrepancies by fitting global material parameters to data; however, when constitutive models are misspecified or observations are sparse, identified parameters often absorb geometry-dependent effects rather than reflect intrinsic material behavior. More expressive constitutive models can improve accuracy but substantially increase computational cost, limiting practicality. We propose a residual acceleration field learning (RAFL) framework that augments a base simulator with a transferable, element-level corrective dynamics field. Operating on shared local features, the model is agnostic to global mesh topology and discretization. Trained end-to-end through a differentiable simulator using sparse marker observations, the learned residual generalizes across shapes. In both sim-to-sim and sim-to-real experiments, our method achieves consistent zero-shot improvements on unseen morphologies, while system identification frequently exhibits negative transfer. The framework also supports continual refinement, enabling simulation accuracy to accumulate during morphology optimization.

Kuang Huang, Dong Heon Cho, Boyuan Chen

Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We introduce a framework that automatically discovers a low-dimensional and operable representation of system dynamics, including a set of compact state variables that preserve the smoothness of the system dynamics and a differentiable vector field, directly from video without requiring prior domain-specific knowledge. The prominence and effectiveness of the proposed approach are demonstrated through both quantitative and qualitative analyses of a range of dynamical systems, including the identification of stable equilibria, the prediction of natural frequencies, and the detection of of chaotic and limit cycle behaviors. The results highlight the potential of our data-driven approach to advance automated scientific discovery.