Vidhyanand (Vick) Mahase PharmD, PhD.’s Post

🚀 Our last paper, "Variational Physics-Informed Neural Operator (VINO) for Solving Partial Differential Equations," is now available at https://lnkd.in/eRWaVAr2 Solving PDEs is crucial for simulating natural and engineering systems. However, the computational cost can be significant. Our research introduces VINO, a novel deep learning approach for solving PDEs by minimizing their energy formulation—enabling training without labeled data and delivering improved performance over existing methods and traditional solvers. Key highlights of VINO: 🔹 Variational format with domain discretization to efficiently evaluate governing equations. 🔹 Enhanced accuracy and performance, particularly as mesh resolution increases. 🔹 Overcomes the challenge of calculating derivatives in physics-informed neural networks/operators.

The literature concerning the use of neural networks to approach partial differential equations has increased significantly in recent years. Most of the results are heuristic and the ability of neural networks to perform better than classical methods is not always clear. Together with researcher at UAM Dr Julia Novo we recently published a short article in Elsevier’s Journal of Computational and Applied Mathematics (JCAM). The aim of the article is to construct a neural network for which the linear finite element approximation of a simple one-dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to reproduce the finite element approximation. The deepest goal is to shed some light on the problems one encounters when trying to use neural networks to approximate partial differential equations.

❓ Is it possible to use Gaussian Processes (GPs) for solving partial differential equations (PDEs)? Yes! In fact, GPs are naturally suited for solving linear PDEs (since the linear transformation of a GP is still a GP!). However, nonlinear PDEs require a bit more work—they need to be linearized before applying GP regression. This is where neural networks often have the edge: they can handle nonlinear PDEs directly, without needing linearization. 💡 To bridge this gap, in our recent paper, we propose a new GP-based framework that combines the best of both worlds: the local generalization power of kernels with the flexibility of deep neural networks. 🗝️ The resulting model is particularly attractive because (1) it automatically satisfies linear constraints (like boundary and initial conditions) thanks to the inherent structure of kernels, and (2) it can integrate any differentiable function approximator—including neural networks— into the GP's mean function, making it highly adaptable for nonlinear constraints. Through a diverse set of examples, we found that our approach not only outperforms but also enhances existing physics-informed machine learning methods that depend solely on neural networks. A special thanks to my labmates Amin Yousefpour and Shirin Hosseinmardi, and my advisor Ramin Bostanabad for their invaluable support! Check out the full paper and code below: 📄 Paper: https://lnkd.in/gMZpD7sn 💻 Code: https://lnkd.in/gfgrqUuC

Researchers at Princeton and IIT Madras used deep learning and evolutionary algorithms to design high-performance integrated circuits for wireless communications. By training convolutional neural networks (CNNs) on circuit design simulations, they generated and optimized new designs faster than traditional methods. The new designs defied conventional engineering intuition but performed well, completing in minutes what usually takes weeks. Read our summary of the paper in The Batch: https://hubs.la/Q033_Hmf0

🚀 Revolutionizing AI with Geometric Algebra, Hyperdimensional Computing, and Spiking Neural Networks 🧠✨ What happens when you merge Geometric Algebra for precise spatial reasoning, Hyperdimensional Computing (HDC) for robust high-dimensional representations and Spiking Neural Networks (SNNs) for bio-inspired temporal dynamics? You get a Geometric Algebra Neural Network (GANN) integrated with Spiking Neural Field Computing and a fractal-inspired architecture! 🌌 This isn't just another neural network – it's a paradigm shift: 🔹 Geometric Algebra elegantly handles multivectors, unifying algebraic and geometric operations for spatial computation. 🔹 HDC enables noise-tolerant, efficient, and compositional representations in 10,000+ dimensions. 🔹 Spiking Neural Networks bring the temporal precision and biological fidelity of real neurons. 🔹 Fractal Networks introduce recursive, modular structures, enabling scalability and efficiency. The result? A system that blends mathematics, cognitive science and scalable computing for next-generation AI models. Imagine applications in robotics, vision, temporal reasoning and more – all while pushing the boundaries of what neural architectures can achieve. This is AI inspired by the brain's genius and geometry's elegance. Dive into the details and learn how we made this possible🔗 Let’s discuss – where else do you see this revolutionary approach transforming AI? #ArtificialIntelligence #GeometricAlgebra #HyperdimensionalComputing #SpikingNeuralNetworks #FractalComputing #NeuralNetworks #CognitiveAI #InnovativeAI #MachineLearning

Great combinations between Neural Network and Physics laws. i as the graduated student of physics and computer science master degree really proud to have an ability to deep dive my knowledge

Physics-Informed Neural Networks (PINNs) – a groundbreaking approach that leverages the power of neural networks to solve complex differential equations by integrating physical laws directly into the learning process. #AI #MachineLearning #Physics #NeuralNetworks #Research

Thanks Raj Abhijit Dandekar for not keep it a Raj anymore :P #humor . Applying basics of physics is so important in training a CVPR based models on neural network Also learning from #Tesla's CVPR now applying in real life real sense. #CVPR #ProActivFC #Badminton #Growth #Engineering #Health #Science #Thermodynamics

A paper from NEC has been accepted to NeurIPS 2024, a leading conference in artificial intelligence. Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees Authers：Taiki Miyagawa(NEC), Takeru Yokota（Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN Quantum Computing） NeurIPS 2024. Accepted on September 26, 2024 URL: https://lnkd.in/guzTUQQn Abstract: We propose the first learning scheme to solve functional differential equations, built on the physics-informed neural network. 関数の関数、つまり汎関数を解に持つ汎関数微分方程式の、汎用かつ 計算効率の良い世界初のソルバーを提案しました。 #NEC #NeurIPS #AI