David Hyde

Harsh Vardhan, David Hyde, Umesh Timalsina et al.

Physics simulations like computational fluid dynamics (CFD) are a computational bottleneck in computer-aided design (CAD) optimization processes. To overcome this bottleneck, one requires either an optimization framework that is highly sample-efficient, or a fast data-driven proxy (surrogate model) for long-running simulations. Both approaches have benefits and limitations. Bayesian optimization is often used for sample efficiency, but it solves one specific problem and struggles with transferability; alternatively, surrogate models can offer fast and often more generalizable solutions for CFD problems, but gathering data for and training such models can be computationally demanding. In this work, we leverage recent advances in optimization and artificial intelligence (AI) to explore both of these potential approaches, in the context of designing an optimal unmanned underwater vehicle (UUV) hull. Our study finds that the Bayesian Optimization-Lower Condition Bound (BO-LCB) algorithm is the most sample-efficient optimization framework and has the best convergence behavior of those considered. Subsequently, we show that our DNN-based surrogate model predicts drag force on test data in tight agreement with CFD simulations, with a mean absolute percentage error (MAPE) of 1.85%. Combining these results, we demonstrate a two-orders-of-magnitude speedup (with comparable accuracy) for the design optimization process when the surrogate model is used. To our knowledge, this is the first study applying Bayesian optimization and DNN-based surrogate modeling to the problem of UUV design optimization, and we share our developments as open-source software.

Ayano Kaneda, Osman Akar, Jingyu Chen et al.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the $L^2$ difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

Huy Tran, Max Milkert, David Hyde

Doubly-stochastic attention has emerged as a transport-based alternative to row-softmax attention, with recent Transformer variants using it to reduce attention sinks and rank collapse while improving performance. In this family, the standard approach is Sinkhorn scaling, which trains more efficiently but still repeats matrix scaling in every inference forward pass. Sliced-transport attention removes the online iteration, but its soft sorting approximation materializes dense tensors for each slice, requiring substantially more training resources than Sinkhorn attention. We introduce ASAP: Amortized Doubly-Stochastic Attention via Sliced Dual Projection, a train-then-compile method that trains the doubly-stochastic layer with Sinkhorn, then replaces the iterative scaling loop at inference with a fixed sliced-dual operator. It learns a lightweight parametric map from exact one-dimensional Kantorovich potentials to the Sinkhorn query-side dual, then reconstructs the attention plan with a two-sided entropic c-transform. Across language and vision benchmarks, ASAP keeps the cheaper training setup and remains highly competitive with recent baselines. In the main frozen-layer benchmark, ASAP is 5.3 faster than the trained Sinkhorn teacher while matching its accuracy; in downstream replacements, ASAP recovers most of the teacher performance without any retraining.

Manish Acharya, David Hyde

Dynamic tetrahedral simulation pipelines rebuild topology-dependent solver state after every fracture, refinement, or merge event - discarding structural continuity that survives each edit and spending global work on what are often local changes. We present STA-FEM, a streaming assembly method for simulations with topologically-dynamic tetrahedral meshes operating on a fixed superset mesh: when the candidate element pool is preallocated and the per-frame edit stream is exposed, the surrounding solver, preconditioner, and time-stepping layers stay unchanged while the per-frame assembly step is replaced with persistent incremental updates that match a full-rebuild approach exactly at every frame. Across various three-dimensional examples with up to 460k elements, the method delivers end-to-end speedups of 1.37x to 1.61x over full-rebuild with orders-of-magnitude reductions in matrix update cost, preserving exact matrix parity in all tested frames against a stronger exact local recomputation baseline. We test our algorithm in realistic fracture simulation pipelines and observe up to 76% speedups in fracture frame time with exact equivalence to a ground-truth full-rebuild algorithm. These results establish exact streaming assembly as a potentially practical approach for simulating tetrahedral meshes with dynamic topology.

Harsh Vardhan, Umesh Timalsina, Michael Sandborn et al.

In this work, we introduce an open-source integrated CAD-CFD tool, Anvil, which combines FreeCAD for CAD modeling and OpenFOAM for CFD analysis, along with an AI-based optimization method (Bayesian optimization) and other sampling algorithms. Anvil serves as a scientific machine learning tool for shape optimization in three modes: data generation, CFD evaluation, and shape optimization. In data generation mode, it automatically runs CFD evaluations and generates data for training a surrogate model. In optimization mode, it searches for the optimal design under given requirements and optimization metrics. In CFD mode, a single CAD file can be evaluated with a single OpenFOAM run. To use Anvil, experimenters provide a JSON configuration file and a parametric CAD seed design. Anvil can be used to study solid-fluid dynamics for any subsonic flow conditions and has been demonstrated in various simulation and optimization use cases. The open-source code for the tool, installation process, artifacts (such as CAD seed designs and example STL models), experimentation results, and detailed documentation can be found at \url{https://github.com/symbench/Anvil}.

Chang-Yong Song, David Hyde

Differentiable particle-based simulation can produce physically plausible motion, but target-driven volumetric shape morphing remains underconstrained: physics-only mass matching captures coarse global structure yet struggles with fine geometric detail, while naive image-space coupling destabilizes elastic dynamics. We present PhysMorph-GS, a render-guided morphing framework that couples material point method simulation with differentiable 3D Gaussian splatting. The key idea is to inject visual supervision through the deformation gradient $\mathbf{F}$ rather than particle positions, so render gradients act as control-space guidance while trajectories remain governed by physics. We further introduce phased Chamfer-guided plasticity that delays rest-state migration until coarse structure has formed; in practice, rendering is evaluated on a surface-focused particle subset for efficiency and gradient concentration. Relative to a physics-only baseline, our method reduces silhouette error by 25.8\%, 10.8\%, and 49.9\% on representative examples, with the largest gains on models with thin features. These results suggest that the main challenge in render-guided differentiable morphing is not simply adding stronger image losses, but injecting visual guidance in a way that remains compatible with elastic simulation. We further observe that plasticity-driven rest-state migration drives different sources toward a shared target-determined attractor, distinguishing physics-based morphing from interpolation between registered shape pairs.

Max Milkert, David Hyde, Forrest Laine

In a neural network with ReLU activations, the number of piecewise linear regions in the output can grow exponentially with depth. However, this is highly unlikely to happen when the initial parameters are sampled randomly, which therefore often leads to the use of networks that are unnecessarily large. To address this problem, we introduce a novel parameterization of the network that restricts its weights so that a depth $d$ network produces exactly $2^d$ linear regions at initialization and maintains those regions throughout training under the parameterization. This approach allows us to learn approximations of convex, one dimensional functions that are several orders of magnitude more accurate than their randomly initialized counterparts. We further demonstrate a preliminary extension of our construction to multidimensional and non-convex functions, allowing the technique to replace traditional dense layers in various architectures.

Chang-Yong Song, David Hyde

Chamfer distance is the standard training loss for point cloud reconstruction, completion, and generation, yet directly optimizing it can produce worse Chamfer values than not optimizing it at all. We show that this paradoxical failure is gradient-structural. The per-point Chamfer gradient creates a many-to-one collapse that is the unique attractor of the forward term and cannot be resolved by any local regularizer, including repulsion, smoothness, and density-aware re-weighting. We derive a necessary condition for collapse suppression: coupling must propagate beyond local neighborhoods. In a controlled 2D setting, shared-basis deformation suppresses collapse by providing global coupling; in 3D shape morphing, a differentiable MPM prior instantiates the same principle, consistently reducing the Chamfer gap across 20 directed pairs with a 2.5$\times$ improvement on the topologically complex dragon. The presence or absence of non-local coupling determines whether Chamfer optimization succeeds or collapses. This provides a practical design criterion for any pipeline that optimizes point-level distance metrics.

Elizabeth G. Campolongo, Yuan-Tang Chou, Ekaterina Govorkova et al.

Scientific discoveries are often made by finding a pattern or object that was not predicted by the known rules of science. Oftentimes, these anomalous events or objects that do not conform to the norms are an indication that the rules of science governing the data are incomplete, and something new needs to be present to explain these unexpected outliers. The challenge of finding anomalies can be confounding since it requires codifying a complete knowledge of the known scientific behaviors and then projecting these known behaviors on the data to look for deviations. When utilizing machine learning, this presents a particular challenge since we require that the model not only understands scientific data perfectly but also recognizes when the data is inconsistent and out of the scope of its trained behavior. In this paper, we present three datasets aimed at developing machine learning-based anomaly detection for disparate scientific domains covering astrophysics, genomics, and polar science. We present the different datasets along with a scheme to make machine learning challenges around the three datasets findable, accessible, interoperable, and reusable (FAIR). Furthermore, we present an approach that generalizes to future machine learning challenges, enabling the possibility of large, more compute-intensive challenges that can ultimately lead to scientific discovery.

Shihan Cheng, Nilesh Kulkarni, David Hyde et al.

Fine-tuning large-scale text-to-video diffusion models to add new generative controls, such as those over physical camera parameters (e.g., shutter speed or aperture), typically requires vast, high-fidelity datasets that are difficult to acquire. In this work, we propose a data-efficient fine-tuning strategy that learns these controls from sparse, low-quality synthetic data. We show that not only does fine-tuning on such simple data enable the desired controls, it actually yields superior results to models fine-tuned on photorealistic "real" data. Beyond demonstrating these results, we provide a framework that justifies this phenomenon both intuitively and quantitatively.

Manish Acharya, David Hyde

The sliced Wasserstein distance (SW) reduces optimal transport on $\mathbb{R}^d$ to a sum of one-dimensional projections, and thanks to this efficiency, it is widely used in geometry, generative modeling, and registration tasks. Recent work shows that quasi-Monte Carlo constructions for computing SW (QSW) yield direction sets with excellent approximation error. This paper presents an alternate, novel approach: learning directions with Bayesian optimization (BO), particularly in settings where SW appears inside an optimization loop (e.g., gradient flows). We introduce a family of drop-in selectors for projection directions: BOSW, a one-shot BO scheme on the unit sphere; RBOSW, a periodic-refresh variant; ABOSW, an adaptive hybrid that seeds from competitive QSW sets and performs a few lightweight BO refinements; and ARBOSW, a restarted hybrid that periodically relearns directions during optimization. Our BO approaches can be composed with QSW and its variants (demonstrated by ABOSW/ARBOSW) and require no changes to downstream losses or gradients. We provide numerical experiments where our methods achieve state-of-the-art performance, and on the experimental suite of the original QSW paper, we find that ABOSW and ARBOSW can achieve convergence comparable to the best QSW variants with modest runtime overhead.

Michael Bao, David Hyde, Xinru Hua et al.

It is well known that popular optimization techniques can lead to overfitting or even a lack of convergence altogether; thus, practitioners often utilize ad hoc regularization terms added to the energy functional. When carefully crafted, these regularizations can produce compelling results. However, regularization changes both the energy landscape and the solution to the optimization problem, which can result in underfitting. Surprisingly, many practitioners both add regularization and claim that their model lacks the expressivity to fit the data. Motivated by a geometric interpretation of the linearized search space, we propose an approach that ameliorates overfitting without the need for regularization terms that restrict the expressiveness of the underlying model. We illustrate the efficacy of our approach on minimization problems related to three-dimensional facial expression estimation where overfitting clouds semantic understanding and regularization may lead to underfitting that misses or misinterprets subtle expressions.