Extends structural identifiability analysis to functional components of differential equation models and characterizes conditions for unique recovery using differential algebra techniques.
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Universal Differential Equations for Scientific Machine Learning
48 Pith papers cite this work, alongside 71 external citations. Polarity classification is still indexing.
48
Pith papers citing it
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abstract
In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approaches. We describe a mathematical object, which we denote universal differential equations (UDEs), as the unifying framework connecting the ecosystem. We show how a wide variety of applications, from automatically discovering biological mechanisms to solving high-dimensional Hamilton-Jacobi-Bellman equations, can be phrased and efficiently handled through the UDE formalism and its tooling. We demonstrate the generality of the software tooling to handle stochasticity, delays, and implicit constraints. This funnels the wide variety of SciML applications into a core set of training mechanisms which are highly optimized, stabilized for stiff equations, and compatible with distributed parallelism and GPU accelerators.
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cs.LG 20 quant-ph 4 cs.AI 3 eess.SY 3 math.NA 3 physics.flu-dyn 2 astro-ph.IM 1 cs.CV 1 cs.NE 1 cs.RO 1roles
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AgentODE uses LLMs to discover ODE structures and infer parameter distributions from aggregate data, recovering consistent structures on benchmarks and RDEB clinical data with 231 observations from 46 patients.
A nudged-system optimization method recovers parameters in the Lorenz-63 system from partial noisy observations, with theoretical guarantees on synchronization and identifiability.
ASYS recovers known analytical PDE forms and generates new interpretable symbolic approximations, such as a geometric interface formula for 2D Allen-Cahn and a nine-parameter contraction law for Keller-Segel blow-up, via agent-guided evolutionary search on differentiable programs.
Randomized Jacobian matching implicitly enforces second-order consistency in learned chaotic vector fields at O(d^2) cost without forming the full Hessian.
The Neural Compiler converts symbolic programs into exact differentiable PyTorch modules for hybrid scientific machine learning, enabling precise encoding of known physics with few trainable parameters.
Mechanistic priors reduce Bayesian regret in sequential decisions by scaling with residual entropy H_mech, yielding a sample complexity reduction of H(μ)/H_mech asymptotically and lower bounds on penalties in the burn-in regime, with gains shown in 5-FU dosing simulations.
A residual-corrected ECM-UDE hybrid model outperforms standalone ECM and LSTM baselines in battery terminal voltage prediction, with the largest gains under temperature and drive-cycle distribution shifts.
NOVA represents world states as INR weights for decoder-free rendering, compactness, and unsupervised disentanglement of background, foreground, and motion in video world models.
AegirJAX embeds a coastal hydrodynamics solver as a continuous computational graph in JAX to enable end-to-end optimization and inversion for bathymetry recovery, breakwater design, wave cancellation, and model correction.
A universal shallow water equations solver integrates neural networks via differentiable programming to enable inverse modeling of flow resistance and physics discovery in river channels.
Paper-replication makes coding agents complete SciML paper replications only when every recorded claim has provenance, comparison evidence, and report coverage in a validated workspace.
LSTM on latent manifold jointly predicts dynamics and optimizes control pulses, cutting optimization cost by 1000x on adiabatic speedup and noisy spin-chain transfer tasks.
Mosaic is a benchmark suite evaluating 14 differentiable PDE solvers across fluids, structures, and heat transfer, showing large variations in cost and conditioning but similar convergence behavior.
A differentiable composite approximation framework jointly calibrates polynomial and neural components for improved recursive AUV trajectory and velocity prediction from field data with current compensation.
OrthoReg penalizes overlap between symbolic and neural components in hybrid dynamical models, improving symbolic recovery and out-of-distribution behavior under partial library mismatch.
A hybrid SINDy plus neural ODE grey-box framework extracts continuous-time analytical surrogates from 40-year system dynamics simulations of electric freight transitions, achieving NRMSE below 4% on training data and reliable predictions on unseen initial conditions.
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
FNO exhibits strong frequency bias with sharp OOD error growth on high-frequency inputs in wave equations, while DeepONet shows milder degradation despite higher baseline error.
BINNs are extended to 2D+t systems and combined with symbolic regression to recover reaction-diffusion models of lung cancer cell dynamics from time-lapse microscopy data.
DiLaR-PINN learns dissipative effects in electromechanical systems via a skew-dissipative latent residual PINN that guarantees non-increasing energy and uses recurrent curriculum training for partial observations.
LASS-ODE-Power is a pretrained model that predicts power-system dynamic trajectories across regimes in a zero-shot manner after large-scale ODE pretraining and targeted fine-tuning.
A physics-informed neural representation is learned from safe data to support distributional hypothesis testing for dynamical instability in stochastic DAE systems without repeated simulations.
A PINN learns higher-order corrections to the TaylorT4 PN model from eight NR surrogate waveforms, reducing phase and amplitude errors in the inspiral while enforcing physical symmetries.
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