arXiv subjects

Nikola Borislavov Kovachki

Publications and source records attributed to Nikola Borislavov Kovachki.

3 recordsLinked to original sources

arXiv2026

CANTO: CAD-Native Transformer Operators for AI-Aided Engineering

Modern engineering systems, from automobiles to aircraft, are designed by using precise, continuous parametric computer-aided design (CAD) models. Evaluating design changes through numerical simulation requires meshing the continuous geometry, a computationally expensive and often brittle process that can require manual intervention and replaces the continuous representation with a discrete approximation. Most neural surrogates accelerate the simulation, but inherit this representation gap by relying on meshes, point clouds, voxels, or other sampled approximations of geometry. We introduce CANTO, a transformer neural operator that maps directly from continuous CAD geometry to physical fields, without meshing the input geometry. We develop a theoretical framework for learning operators from geometric manifolds to function spaces of physical fields, representing geometry through sequences of parametric patches. CANTO instantiates this framework by directly tokenizing non-uniform rational B-spline (NURBS) patches from their control points, knot vectors, and weights, and predicts continuous surface and volume fields at arbitrary query locations. We evaluate CANTO on four automotive and aircraft aerodynamics industry benchmarks: AhmedML, WindsorML, DrivAerML, and HiLiftAeroML. CANTO achieves state-of-the-art accuracy on most evaluated surface and volume prediction tasks, including a 19.8% reduction in surface-pressure relative $L_2$ error compared with AB-UPT on HiLiftAeroML. Differentiability with respect to CAD parameters further enables gradient-based inverse design of designs. On AhmedML, CANTO identifies designs with 4.4 to 20.4% lower drag than the best dataset designs satisfying the same volume and lift constraints, with the improvements verified using the same CFD setup used to generate the original dataset.

cs.AI↗

arXiv2024

Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Models

Using image models naively for solving inverse video problems often suffers from flickering, texture-sticking, and temporal inconsistency in generated videos. To tackle these problems, in this paper, we view frames as continuous functions in the 2D space, and videos as a sequence of continuous warping transformations between different frames. This perspective allows us to train function space diffusion models only on images and utilize them to solve temporally correlated inverse problems. The function space diffusion models need to be equivariant with respect to the underlying spatial transformations. To ensure temporal consistency, we introduce a simple post-hoc test-time guidance towards (self)-equivariant solutions. Our method allows us to deploy state-of-the-art latent diffusion models such as Stable Diffusion XL to solve video inverse problems. We demonstrate the effectiveness of our method for video inpainting and $8\times$ video super-resolution, outperforming existing techniques based on noise transformations. We provide generated video results: https://giannisdaras.github.io/warped_diffusion.github.io/.

cs.CV↗

arXiv2023

Geometry-Informed Neural Operator for Large-Scale 3D PDEs

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and point-cloud representations of the input shape and neural operators based on graph and Fourier architectures to learn the solution operator. The graph neural operator handles irregular grids and transforms them into and from regular latent grids on which Fourier neural operator can be efficiently applied. GINO is discretization-convergent, meaning the trained model can be applied to arbitrary discretization of the continuous domain and it converges to the continuum operator as the discretization is refined. To empirically validate the performance of our method on large-scale simulation, we generate the industry-standard aerodynamics dataset of 3D vehicle geometries with Reynolds numbers as high as five million. For this large-scale 3D fluid simulation, numerical methods are expensive to compute surface pressure. We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points. The cost-accuracy experiments show a $26,000 \times$ speed-up compared to optimized GPU-based computational fluid dynamics (CFD) simulators on computing the drag coefficient. When tested on new combinations of geometries and boundary conditions (inlet velocities), GINO obtains a one-fourth reduction in error rate compared to deep neural network approaches.

cs.LG↗