Physics-Informed Neural Networks — 12 Technical Articl…

Apr 22, 2026 · Artificial Intelligence

Solving the Burgers Equation with TINN: High‑Precision Physics‑Informed Neural Networks in 380 seconds

This tutorial presents the Time‑Induced Neural Network (TINN) framework that overcomes the time‑entanglement issue of standard PINNs by introducing a dedicated time‑subnet with FiLM modulation, employs a Levenberg‑Marquardt optimizer for second‑order updates, and demonstrates a 1e‑6 relative error solution of the 1‑D viscous Burgers equation in just 371 seconds on an RTX 4090.

Burgers EquationFiLM ModulationJAX

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Solving the Burgers Equation with TINN: High‑Precision Physics‑Informed Neural Networks in 380 seconds

AI Agent Research Hub

Apr 1, 2026 · Artificial Intelligence

Scale‑PINN Solves High‑Re Navier‑Stokes in 100 seconds, Cutting Error by 96 %

The tutorial introduces Scale‑PINN, which adds an evolutionary regularization term inspired by pseudo‑time stepping to the PINN loss, enabling a shared‑backbone network to solve the lid‑driven cavity Navier‑Stokes problem at Re = 7500 in about 100 seconds and reducing the relative velocity error by roughly 96 % compared with a standard PINN.

Evolutionary regularizationHigh Reynolds numberJAX

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Scale‑PINN Solves High‑Re Navier‑Stokes in 100 seconds, Cutting Error by 96 %

Bighead's Algorithm Notes

Mar 27, 2026 · Artificial Intelligence

Weekly Quantitative Finance Paper Roundup (Mar 21‑27, 2026)

This article presents concise English summaries of four recent AI‑driven quantitative finance papers, covering an agentic AI screening platform for portfolio investment, a wavelet‑based physics‑informed neural network for option pricing, the FinRL‑X modular trading infrastructure, and the S³G stock state‑space graph for enhanced trend prediction, each with authors, links, and key experimental results.

AILLMModular Trading Infrastructure

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Weekly Quantitative Finance Paper Roundup (Mar 21‑27, 2026)

AI Agent Research Hub

Mar 25, 2026 · Industry Insights

2026 Guide to Choosing Journals for Physics-Informed Neural Networks (PINNs)

This article provides a concise reference of 21 common PINN journals, organized by region and TOP status, and offers practical advice on matching your research to the right audience rather than chasing journal rankings.

Academic PublishingArtificial IntelligenceJournal Selection

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2026 Guide to Choosing Journals for Physics-Informed Neural Networks (PINNs)

AI Agent Research Hub

Mar 18, 2026 · Artificial Intelligence

Variable-Scaling PINN for 2D Navier‑Stokes: How Coordinate Rescaling Improves Stiff PDE Training

This tutorial explains how a simple coordinate scaling (VS‑PINN) reduces stiffness in physics‑informed neural networks, demonstrates its implementation in JAX for the 2D steady incompressible Navier‑Stokes cylinder‑flow benchmark, and shows that after 80 000 Adam iterations the relative errors drop to 2.10 % (u), 5.06 % (v) and 4.45 % (p).

JAXNavier-StokesPINN

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Variable-Scaling PINN for 2D Navier‑Stokes: How Coordinate Rescaling Improves Stiff PDE Training

AI Agent Research Hub

Mar 16, 2026 · Artificial Intelligence

How NTK Adaptive Weighting and Multi‑Scale Fourier Features Enable PINNs to Solve High‑Frequency PDEs

This tutorial explains why standard physics‑informed neural networks fail on high‑frequency partial differential equations due to spectral bias, and demonstrates how random Fourier feature embeddings, multi‑scale concatenation or spatio‑temporal separation, and Neural Tangent Kernel‑based adaptive loss weighting together overcome the bias and achieve accurate, stable solutions for heat, Poisson, and wave equations using JAX.

Fourier FeaturesJAXMulti-Scale

0 likes · 23 min read

How NTK Adaptive Weighting and Multi‑Scale Fourier Features Enable PINNs to Solve High‑Frequency PDEs

AI Agent Research Hub

Feb 26, 2026 · Artificial Intelligence

Can PINNs Reconstruct Velocity and Pressure Fields from Passive Scalar Visualizations?

This article analyzes the Science paper that uses physics‑informed neural networks (HFM) to infer complete velocity and pressure fields from only passive scalar concentration data such as smoke or dye, detailing the mathematical formulation, network architecture, training strategy, benchmark results, robustness studies, and the method’s limitations and broader impact.

Fluid MechanicsPINNsPassive Scalar

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Can PINNs Reconstruct Velocity and Pressure Fields from Passive Scalar Visualizations?

AI Algorithm Path

Oct 13, 2025 · Artificial Intelligence

Step-by-Step Explanation of Neural ODEs with Code Examples

This article introduces Neural Ordinary Differential Equations, explains their core idea of learning continuous dynamics via a neural derivative function, demonstrates Euler integration, compares naive unfolding with the adjoint method for training, provides a PyTorch implementation, and offers practical tips and extensions such as event handling and physics‑informed models.

Adjoint methodContinuous-time modelingEuler method

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Step-by-Step Explanation of Neural ODEs with Code Examples

Data Party THU

Oct 4, 2025 · Artificial Intelligence

How DeepMind’s AI Uncovered New Unstable Singularities in Fluid Dynamics

DeepMind, together with researchers from NYU, Stanford and Brown, used physics‑informed neural networks, a Gauss‑Newton optimizer and multi‑stage training to systematically discover previously unknown unstable singularities in three fluid‑dynamics equations, revealing a concise asymptotic formula linking blow‑up rates to instability order.

DeepMindGauss-Newton optimizerPhysics-Informed Neural Networks

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How DeepMind’s AI Uncovered New Unstable Singularities in Fluid Dynamics

HyperAI Super Neural

Sep 19, 2025 · Artificial Intelligence

DeepMind Uses AI to Uncover New Unstable Singularities in Three Fluid Equations

Google DeepMind, together with researchers from NYU, Stanford and Brown, applied a machine‑learning framework and a high‑precision Gauss‑Newton optimizer to systematically discover new unstable singularities in three fluid equations, achieving solution accuracy that significantly surpasses existing work and revealing an empirical formula linking blow‑up rate to instability order.

DeepMindGauss-Newton optimizerNavier-Stokes

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DeepMind Uses AI to Uncover New Unstable Singularities in Three Fluid Equations

AIWalker

Jul 1, 2025 · Artificial Intelligence

How a Minor Tweak to PINN Achieves Up to 100× Speedup

Recent breakthroughs such as VS‑PINN, Stiff‑PINN, MAD‑Scientist and KAN‑ODEs demonstrate how small algorithmic changes and novel training strategies can accelerate physics‑informed neural networks by orders of magnitude while expanding their applicability to stiff PDEs, chemical kinetics and dynamical systems.

PINNPhysics-Informed Neural NetworksScientific Machine Learning

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How a Minor Tweak to PINN Achieves Up to 100× Speedup

AI Frontier Lectures

Mar 21, 2025 · Artificial Intelligence

How ConFIG Eliminates Gradient Conflicts for Faster Multi‑Task Deep Learning

The paper introduces ConFIG (Conflict‑Free Inverse Gradients), a mathematically proven method that resolves gradient conflicts among multiple loss terms in physics‑informed neural networks, multi‑task learning, and continual learning, and its momentum‑based variant M‑ConFIG that further accelerates training while maintaining accuracy.

CONFIGGradient ConflictM-ConFIG

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How ConFIG Eliminates Gradient Conflicts for Faster Multi‑Task Deep Learning