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Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using…
We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…
Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of the Navier-Stokes equations at Reynolds numbers 3500 and above can generate high-frequency signals…
We introduce a novel computational framework for digital geometry processing, based upon the derivation of a nonlinear operator associated to the total variation functional. Such operator admits a generalized notion of spectral…
Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require…
The design of the nanostructures that are used in the field of nano-photonics has remained complex, very often relying on the intuition and expertise of the designer, ultimately limiting the reach and penetration of this groundbreaking…
Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…
Neural implicit functions have achieved impressive results for reconstructing 3D shapes from single images. However, the image features for describing 3D point samplings of implicit functions are less effective when significant variations…
If robots could reliably manipulate the shape of 3D deformable objects, they could find applications in fields ranging from home care to warehouse fulfillment to surgical assistance. Analytic models of elastic, 3D deformable objects require…
Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…
Advances in robotics, artificial intelligence, and machine learning are ushering in a new age of automation, as machines match or outperform human performance. Machine intelligence can enable businesses to improve performance by reducing…
Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…
This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time…
This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…
The accuracy and fidelity of deformation simulations are highly dependent upon the underlying constitutive material model. Commonly used linear or nonlinear constitutive material models only cover a tiny part of possible material behavior.…
It has been a long-standing materials science challenge to establish structure-property relations in amorphous solids. Here we introduce a rotation-variant local structure representation that enables different predictions for different…
We introduce SDM-NET, a deep generative neural network which produces structured deformable meshes. Specifically, the network is trained to generate a spatial arrangement of closed, deformable mesh parts, which respect the global part…
Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however,…
Applications in fields ranging from home care to warehouse fulfillment to surgical assistance require robots to reliably manipulate the shape of 3D deformable objects. Analytic models of elastic, 3D deformable objects require numerous…
The reconstruction of cortical surfaces from brain magnetic resonance imaging (MRI) scans is essential for quantitative analyses of cortical thickness and sulcal morphology. Although traditional and deep learning-based algorithmic pipelines…