Intrinsic Lie point symmetries discovered from differential equation data
Framework identifies complete generator sets and reproduces Lie-bracket structure from sampled jet-space data.
Stories per day · 30 days
1 RSS
Relateddifferential-equations2neural-networks2conservation-laws1constitutive-modeling1dynamical-systems1e-ude1lie-symmetries1malware-propagation1navier-stokes1neural-deflation1polyconvexity1turbulence1
11 stories, newest first · one card per story
Stories tagged #scientific-machine-learning
E-UDE Model Reduces Malware Propagation Prediction Errors by 66%
The E-UDE framework achieves RMSE of 783.70 and MAE of 421.65 on real-world data while remaining robust to noise.
Paper urges four-dimensional treatment of learned fluid turbulence
Using direct numerical simulations larger than 28 TB per run, the authors find spatial and temporal checks can disagree.
SPCNNs approximate symmetric polyconvex energies by construction
The authors prove universal approximation without isotropy and illustrate stress regression plus a double-well envelope.
Neural method tracks how local conservation laws break down globally
Expanding-domain neural deflation recovers the expected local invariants, then their successive breakdown.
A Response Theory Probe for Learned Stochastic AI Simulators, Tested on Lorenz-63
A response-theory probe tests whether learned chaotic simulators react correctly to forcing on Lorenz-63.
Singular parameters and missing limits in neural PDE solvers
Neural tanh PDE solvers can miss finite limits as parameters diverge; kernel derivatives restore attainable approximations.
PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs
PDE-JEPA uses masked-latent predictive pretraining with geometry alignment for parametric PDE dynamics, beating SOTA by 33.4% in-distribution and 51.4% extrapolating.
Learning Physics from an Imperfect Ancestor
A three-stage method uses an imperfect neural operator to steer PINNs into the correct PDE basin.
PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers
Researchers release PosteriorBench, a benchmark testing whether generative inverse solvers recover full reference posteriors across four physics-based inverse problems.
Local gradient neural operator
Researchers propose LGNO, a lightweight interpretable neural operator using learnable local stencils, matching global-operator accuracy on PDE benchmarks with fewer parameters.