SKG: A Law-Induced Engine from Inference to Induction

Jian An; Chaoshi Wu; Jinhui Wu

cs.LGOct 14, 2026

SKG: A Law-Induced Engine from Inference to Induction

Authors: Jian An, Chaoshi Wu, Jinhui Wu

Abstract

This paper proposes the SKG (Symplectic-Kernel Gradient) reasoning engine for law-induced inference and induction. Laws are a priori; data provide instances. Inference is geometric evolution under law constraints. We organize symplectic geometry, GENERIC, kernel methods, RKHS, group-equivariant networks, and constrained mechanics into a unified, analyzable, implementable, verifiable framework. We propose the SKG octuple S = (M, g, omega, H, S, G, Delta, Pi), whose four components correspond to four levels of laws: conservation laws, constitutive relations, symmetry groups, and axiom systems. Main results: (1) Invariants enter metric construction via the Jacobian: g = J^T Sigma^-1 J + epsilon_G I. For constant cases, we establish inverse reconstruction theory: solvability rank condition (Thm 3.9), consistency criterion (Thm 3.11), and uniqueness theorem (Thm 3.14). (2) The kernel bandwidth matrix is uniquely determined by Fisher information and satisfies task-independence (Thm 3.19). (3) The metric reconstruction error decomposes into four terms (Thm 3.21), with squared condition number kappa(Sigma^*)^2 as the dominant amplification factor (Thm 3.22). (4) For state-dependent cases, we establish function-space reconstruction theory on matrix-valued RKHS (Thms 4.8, 4.9). (5) Three-layer projections handle axiom, symplectic-step, and conservation constraints. (6) The residual equation yields the observable formula, four-dimensional rank condition, and noise propagation, while g_qq is structurally unidentifiable. (7) Kernel parameterization yields the RKHS extrapolation bound (Thm 4.15) and strict OOD gain theorem in group directions (Thm 8.15). (8) The learning-decoupling theorem (Thm 9.1) proves the sole object of induction is the parameters of the task energy. Validation: 1D damped oscillator and 2D rotation-invariant system; 6 unit tests, 10 experiments (paired t-test, p < 0.01).

Figures & tables

Law level	Mathematical object	SKG component	Task relevance
Symmetry group	$G$	$\Delta$	Irrelevant
Axiom system	$\mathcal{A}$	$\Pi$	Irrelevant
Conservation laws	$\omega^{\sharp},E$	$\omega$	Irrelevant
Constitutive relations	$H,S$	$H,S$	Partially relevant

Table 1: Four levels of laws and four SKG components

Aspect	Inference flow	Learning flow
Space	State space $q$	Parameter space $\phi$
Metric	$g_{q}$ (objective, task-independent)	$F_{S}(\phi)$ (task-relevant)
Driving force	$\nabla S$ (energy gradient)	$\nabla\mathcal{L}$ (loss gradient)
Dynamics	$\dot{q}=-g_{q}^{-1}\nabla S$	$\dot{\phi}=-F_{S}^{-1}\nabla\mathcal{L}$
Learning object	None	$\phi$ (parameters of $S_{\text{task}}$ )
Purpose	Reach target	Determine task energy

Table 2: Symmetric structure of inference and learning flows

Dimension	PINN	SKG
Role of laws	Soft regularization	Hard structure
Violating laws	Tolerable (cost is loss)	Mathematically forbidden
OOD guarantee	None	RKHS bound
Constraint handling	Loss term	Three-layer projection
Equivariance	Data augmentation	Structural guarantee
Estimated part	All network parameters	Only parameters of $S_{\text{task}}$

Table 3: Paradigm comparison of SKG and PINN

Component	Mathematical object	Law level	Function
$\omega$	Symplectic form	Conservation law	Geometry of conservative forces
$H,S$	Scalar functions	Constitutive relation	Conservative quantity and dissipative drive
$\Delta$	Invariant map	Symmetry group	Physically important differences
$\Pi$	Projection operators	Axiom system	Allowed states

Table 4: Four components of SKG and levels of laws

$\kappa(\mathcal{A})$	Status	Handling
$<10^{3}$	Numerically stable	Use least squares directly
$10^{3}\leq\kappa(\mathcal{A})<10^{6}$	Regularization needed	Use ridge regression [ 51 , 50 ]
$\geq 10^{6}$	Solution unreliable	Increase embeddings or reduce problem size

Table 5: Condition number criteria

Condition	Recommended method
$M\leq 20$ and small residual	Cholesky parameterization
$M\leq 20$ and large residual	Switch to manifold optimization
$20<M\leq 100$	Manifold optimization
$M>100$	Cholesky parameterization + stochastic gradient

Table 6: Solution method selection

$\kappa$	$\epsilon_{\text{tol}}=0.1$	$\epsilon_{\text{tol}}=0.01$
1	$6\times 10^{2}$	$6\times 10^{4}$
10	$6\times 10^{6}$	$6\times 10^{8}$
100	$6\times 10^{10}$	$6\times 10^{12}$

Table 7

Question	Answer
How many samples are needed?	$N\geq M\kappa^{4}/\epsilon_{\text{tol}}^{2}$
What dominates the error?	Squared condition number $\kappa^{2}$
How to reduce the error?	Reduce condition number $>$ increase samples
When is transfer possible?	Metric is task-independent and distribution family matches
How to decouple?	Metric from Fisher, energy splits into objective and task

Table 7: Engineering criteria for metric reconstruction

Level	Dependency	Origin
Embedding $J(q)$	Depends on $q$	Jacobian of invariants with respect to state
Kernel bandwidth $\Sigma(\Delta)$	Depends on $\Delta$	Covariance varies with position
Intrinsic metric $g_{\Delta}(\Delta)$	Depends on $\Delta$	Cholesky function or kernel expansion

Table 8: Three levels of state dependence

Aspect	Constant $g_{\Delta}$	Function $g_{\Delta}(\cdot)$
Unknown	$M(M+1)/2$ scalars	Infinite-dimensional function
Equation	Linear	Functional equation
Solution	Linear system	Function-space optimization
Solvability	Rank condition	Function-space rank condition

Table 9: Difference between the constant and function cases

Basis function	Form	Suitable for
Gaussian kernel	$\phi_{j}(\Delta)=\exp(-\\|\Delta-\Delta_{j}\\|^{2}/(2\sigma^{2}))$	Local variation
Polynomial	$\phi_{j}(\Delta)=\Delta^{j}$	Smooth variation
Fourier	$\phi_{j}(\Delta)=\exp(i\omega_{j}\cdot\Delta)$	Periodic variation
Neural network	$\phi_{j}(\Delta)=\text{MLP}_{j}(\Delta)$	General case

Table 10: Basis function selection

Operation	Complexity
$g_{\Delta}(\Delta)$ evaluation	$O(M^{2})$
$J(q)$ computation	$O(Md)$
$g_{q}(q)$ computation	$O(M^{2}d+Md^{2})$
Backpropagation	$O(M^{2}d+Md^{2})$

Table 11: Computational complexity

Projection	Symbol	Object	Constraint type
Axiom projection	$\Pi_{A}$	State $z$	Hard constraint
Symplectic-step projection	$P_{\perp}$	Symplectic step $\omega^{\sharp}\nabla H$	Degeneracy condition
Conservation projection	$\Pi_{E}$	State $z$	Energy conservation

Table 12: Structure of the three-layer projections

Operation	Kernel parameterization	MLP parameterization
Parameter count	$O(Mr)$	$O(M^{2})$
Forward computation	$O(M^{2})$	$O(M^{2})$
Backpropagation	$O(M^{2})$	$O(M^{3})$
$\mathcal{R}_{1}$ computation	$O(Mr^{2})$	$O(M^{3})$
Regularization	Analytic form	Requires autodiff

Table 13: Computational complexity comparison

Aspect	Metric determination	Energy determination
Object	$g_{\Delta}$	Parameters $\phi$ of $S_{\text{task}}$
Data	Domain data	Task data
Supervision	Unsupervised	Supervised
Task-relevant	No	Yes
Time	Offline	Online
Method	MLE + Fisher	Natural gradient flow

Table 14: Metric determination vs energy determination

Aspect	Inference flow	Learning flow
Space	State space $q$	Parameter space $\phi$
Metric	$g_{q}$ (objective, task-independent)	$F_{S}(\phi)$ (task-relevant)
Driving force	$\nabla S$ (energy gradient)	$\nabla\mathcal{L}$ (loss gradient)
Dynamics	$\dot{q}=-g_{q}^{-1}\nabla S$	$\dot{\phi}=-F_{S}^{-1}\nabla\mathcal{L}$
Learning object	None	$\phi$ (parameters of $S_{\text{task}}$ )
Purpose	Reach target	Determine task energy

Table 15: Symmetric structure of inference flow and learning flow

Object	Learned?	Task-relevant?
$g_{\Delta}$	No	No
$F_{S}(\phi)$	No	Yes

Table 17

Aspect	Standard ML	SKG learning flow
Metric	Learning object	Unsupervised determination
Estimated parameters	All network parameters	Parameters $\phi$ of $S_{\text{task}}$
Training cost	Related to all parameters	Only related to $\phi$
Transferability	Requires domain adaptation	Metric naturally transferable
Energy decomposition	None	$S_{\text{obj}}+S_{\text{task}}$

Table 16: Comparison with standard machine learning

Bayesian inference	SKG	Meaning
Prior $p(\theta)$	Metric $g_{\Delta}$	Knowledge before the task
Likelihood $p(D\\|\theta)$	Energy $S_{\text{task}}$	Requirement of task data
Posterior $p(\theta\\|D)$	Learned $S_{\text{task}}$	Induction after the task

Table 17: Analogy with Bayesian inference

Statistical physics	SKG	Meaning
Inertial mass	Metric $g_{q}$	Physical property, not a learning object
Hamiltonian	Energy $S$	System dynamics
Temperature	Learning rate $\eta$	External parameter
Free energy	Loss $\mathcal{L}$	Optimization objective

Table 18: Analogy with statistical physics

Question	Answer
Is the metric learned?	No, objectively determined by Fisher
What is the learning object?	Parameters $\phi$ of $S_{\text{task}}$
Is $F_{S}(\phi)$ learned?	No, but task-relevant; estimated once
When is the metric determined?	Offline, before the task begins
How to transfer?	Share $g_{q}$ within the same domain
Training cost?	Only related to the parameter count of $\phi$

Table 19: Engineering criteria for the learning flow

Item	Setting
Training domain (1D)	$q\in[0.5,2.0]$ , $N=20$ trajectories, 500 steps each
OOD domain (1D)	$q\in[2.0,3.0]$ , $p\in[-1,1]$ , 200 test points
Training domain (2D)	$\\|q\\|\in[0.5,1.5]$ , $\theta\in[0,\pi/6]$
OOD domain (2D)	$\theta\in[\pi/2,3\pi/4]$ (pure rotation), $\\|q\\|\in[1.5,2.5]$ (radius extrapolation)

Table 20: Data partition

Quantity	Value
True $g_{2}$	1.5
Mean observed $g_{2}$	1.5000000000
Maximum error	$3.33\times 10^{-15}$

Table 21: T1 results

Quantity	Value
$A$ shape	$(16,7)$
$rank(A)$	7

Table 22: T2 results

$g_{qq}$	Residual
$I$	$[-0.56,-0.60,-1.03,-0.80]$
$2I$	$[-0.56,-0.60,-1.03,-0.80]$
Non-diagonal	$[-0.56,-0.60,-1.03,-0.80]$

Table 23: T3 results

Quantity	Value
$\varepsilon_{pp}M^{-1}p$	$[0.05,0.045]$
Expected $-\partial_{q}\varepsilon_{V}$	$[-0.05,-0.045]$
Numerical $-\partial_{q}\varepsilon_{V}$	$[-0.05,-0.045]$
Maximum error	$4.07\times 10^{-12}$

Table 24: T4 results

$p$	Theoretical $\sigma/\|p\|$	Measured
0.05	2.000	2.001
0.10	1.000	1.002
0.20	0.500	0.500
0.50	0.200	0.200
1.00	0.100	0.100
2.00	0.050	0.050

Table 25: T5 results

Quantity	Value
Maximum error between $\Sigma^{-1}$ and numerical Hessian	$5.90\times 10^{-9}$

Table 26: T6 results

Model	Structure	Parameter count
SKG	$\ddot{q}=-q-g_{2}(q)\dot{q}$	1153
Black-box	$\ddot{q}=f(q,\dot{q})$	1129

Table 27: E1 setup

Model	OOD MSE	Standard deviation
SKG	$0.556$	$0.041$
Black-box	$2.687$	$0.187$
Ratio	$0.21$	—

Table 28: E1 results

Model	Parameterization	Parameter count
Kernel	$g_{2}=\Lambda(q)+\\|U(q)\\|^{2}$	59
MLP	$g_{2}=\text{softplus}(\text{MLP}(q))$	61

Table 29: E2 setup

Model	OOD MSE	Standard deviation
Kernel	$0.220$	$0.041$
MLP	$0.899$	$0.187$
Ratio	$0.24$	—

Table 30: E2 results

Quantity	Value
Mean $\varepsilon_{ID}$	$2.5\times 10^{-2}$
Mean $R^{2}$	$8.7\times 10^{1}$
Mean $\varepsilon_{OOD}$	$6.6\times 10^{-2}$
Mean bound	$1.3\times 10^{-1}$
Tightness ratio	$0.491$

Table 31: E3 results

Method	Structure	$V^{\prime}$ learning	$g_{2}$ learning
Joint	Simultaneous optimization of $V^{\prime}$ and $g_{2}$	MLP	MLP
Independent	Two-stage	MLP (small $p$ )	Constant

Table 32: E4 setup

Method	OOD MSE	Standard deviation	RMSE relative error
Joint	$0.822$	$0.194$	$18.1\%$
Independent	$3.958$	$0.591$	$51.2\%$
Ratio	$0.21$	—	—

Table 33: E4 results

Steps	Model	ID MSE	OOD MSE	OOD/ID ratio
1,000	K	$7.78\times 10^{-6}$	$8.96\times 10^{-6}$	$1.129$
1,000	M	$5.43\times 10^{-4}$	$6.13\times 10^{-2}$	$114.045$
3,000	K	$6.09\times 10^{-7}$	$7.87\times 10^{-7}$	$1.147$
3,000	M	$2.16\times 10^{-4}$	$6.71\times 10^{-2}$	$320.070$
10,000	K	$3.32\times 10^{-8}$	$3.59\times 10^{-8}$	$1.054$
10,000	M	$4.25\times 10^{-5}$	$6.81\times 10^{-2}$	$1674.814$

Table 34: E5 results

Check	Threshold	Result	Judgment
K’s OOD/ID ratio	$<1.5$	$1.05$ – $1.15$	PASS
M’s OOD/ID ratio	$>1.5$	$114$ – $1675$	PASS
$\varepsilon_{\text{OOD}}(K)<\varepsilon_{\text{OOD}}(M)$	Yes	$1/4400$	PASS
M ratio $>$ K ratio	Yes	$100$ – $1600$ times	PASS
Lower bound holds	Yes	0 violations	PASS
Lower bound meaningful	Yes	$0\%$	Trivial

Table 35: E5 judgment

Rotation angle $\theta$	Error $\\|g(Rq)-Rg(q)R^{\top}\\|$
0.3 rad	$<10^{-6}$
0.7 rad	$<10^{-6}$
1.2 rad	$<10^{-6}$

Table 36: E6 results

Model	Intrinsic metric
Const	$g_{\Delta}$ constant (Chapter 3 model)
Func	$g_{\Delta}(\cdot)$ learned by MLP (Chapter 4 model)
MLP	Unstructured MLP control

Table 37: E7 setup

Model	OOD MSE	Relative to Func
Const	$2.09\times 10^{-2}$	$26\%$
Func	$5.37\times 10^{-3}$	—
MLP	$8.38\times 10^{-3}$	$64\%$

Table 38: E7 results

Metric	Func	Const	Ratio
Interpolation error	$0.34\%$	$10.39\%$	$1/31$
Extrapolation error	$16.30\%$	$41.80\%$	$1/2.6$

Table 39: E8 results

Seed	$\varepsilon_{ID}$	$\varepsilon_{\text{OOD}}$	bound	ratio
0	$<10^{-6}$	$<10^{-5}$	$>10^{-2}$	$<10^{-3}$
1	$<10^{-6}$	$<10^{-5}$	$>10^{-2}$	$<10^{-3}$
2	$<10^{-6}$	$<10^{-5}$	$>10^{-2}$	$<10^{-3}$

Table 40: E9 results

Seed	SKG learning flow (1 parameter)	Standard MLP (1185 parameters)
0	$1.1401\times 10^{0}$	$1.5497\times 10^{0}$
1	$1.1568\times 10^{0}$	$2.0412\times 10^{0}$
2	$1.6467\times 10^{0}$	$2.4470\times 10^{0}$
3	$2.0272\times 10^{0}$	$2.5252\times 10^{0}$
4	$1.4612\times 10^{0}$	$1.9594\times 10^{0}$

Table 41: E10 per-seed OOD MSE

Method	Parameter count	OOD MSE (mean $\pm$ std)
SKG learning flow	1	$\mathbf{1.4864\pm 0.3309}$
Standard MLP	1185	$2.1045\pm 0.3542$
Ratio	$1/1185$	$0.706$

Table 42: E10 summary

Experiment	Validation target	Result	Key value
T1	Proposition 6.3 1D observable	PASS	Error $3.33\times 10^{-15}$
T2	Proposition 6.4 4D rank condition	PASS	$rank=7$
T3	Proposition 6.6 $g_{qq}$ unidentifiable	PASS	Residual independent of $g_{qq}$
T4	Proposition 6.7 Potential–metric coupling	PASS	Error $4.07\times 10^{-12}$
T5	Proposition 6.5 Noise propagation	PASS	Max error $1.48\%$
T6	Theorem 3.4 Kernel Hessian metric	PASS	Error $5.90\times 10^{-9}$

Table 43: Experimental summary

Dimension	Existing methods	SKG
Role of laws	Soft regularization or architectural constraint	Hard structure
Violating laws	Tolerable (cost is loss)	Mathematically forbidden
OOD guarantee	None or partial	RKHS bound
Constraint handling	Loss term or architecture design	Three-layer projection
Equivariance	Data augmentation or architecture design	Structural guarantee
Learning object	All network parameters	Only parameters $\phi$ of $S_{\text{task}}$

Table 44: Paradigm comparison of SKG and existing methods

SKG component	General form	Application examples
Symplectic structure $\omega$	Known conservation law	Mechanics, electromagnetism, quantum mechanics [ 16 , 18 ]
Energy $H,S$	Known constitutive relation	Material models, potential functions
Invariants $\Delta$	Symmetry group representation	Rotation, translation, scale, permutation
Projections $\Pi$	Constraint handling	Hard constraints, conservation laws, gauge fixing [ 31 , 32 ]
Estimated metric $g$	Unknown dissipation/source	Damping, friction, diffusion
Intrinsic metric $g_{\Delta}(\cdot)$	Coordinate-free form of $g$	Transfer learning, OOD distance

Table 45: General forms of SKG components

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Order	Expression	Geometric quantity
0	$\kappa(\Delta)$	Kernel value
2	$\partial_{a}\partial_{b}\kappa\|_{0}=-\Sigma^{-1}_{ab}$	Covariant metric $g_{\Delta}=\Sigma^{-1}$
3	$\partial_{a}\partial_{b}\partial_{c}\kappa\|_{0}=0$	Even function, zero
4	$\partial_{a}\partial_{b}\partial_{c}\partial_{d}\kappa\|_{0}=\Sigma^{-1}_{ab}\Sigma^{-1}_{cd}+\Sigma^{-1}_{ac}\Sigma^{-1}_{bd}+\Sigma^{-1}_{ad}\Sigma^{-1}_{bc}$	Seed of curvature

Appendix

Table 46: Derivative hierarchy of the kernel function

Operation	Complexity
$\partial_{k}g_{q}$	$O(M^{2}d+Md^{2})$
$g_{q}^{-1}$	$O(d^{3})$
$\Gamma^{i}_{jk}$	$O(d^{4})$
$\partial_{k}\Gamma^{i}_{jl}$	$O(d^{5})$
$R^{\rho}_{\ \sigma\mu\nu}$	$O(d^{4})$ (number of components)

Appendix

Table 47: Computational complexity of connection and curvature

Concept	Existing literature	SKG’s advance
Kernel to metric	Standard Hessian metric [ 23 , 24 ]	Systematized for inference
Connection and curvature	Riemannian geometry standard [ 22 , 21 ]	Related to kernel higher-order derivatives
Curvature of Hessian metrics	Information geometry [ 23 , 24 ]	Applied to OOD analysis
Curvature and generalization	Partial work	Heuristic connection, unproven

Appendix

Table 48: Relation to existing literature

Physics-Informed ML

Physics-informed machine learning combines data-driven models with physical laws to solve, predict, and infer scientific systems.

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Oct 23, 2026

SKG in Practice: OOD Generalization Cases Across FourDomains

This paper presents the engineering implementation methods of the SKG inference framework and provides complete case studies across four domains. Case 1, 2D Dissipative Mechanical System: OOD MSE is 1.69 to 4.12 times lower than the best neural baseline; the state-dependent metric yields a 10^8-order improvement under controlled conditions. Case 2, Target Detection Sim-to-Real: Real-machine mAP increases from 0.2564 to 0.4964 (+24.00 points, single-run experiment, 32 images, point estimate), and AP75 increases from 0.1736 to 0.5765 (+40.29 points), with no real-machine retraining required. Case 3, Sequence Modeling sine to square: OOD MSE is 0.0296 versus Transformer 0.0641 (mean of 5 seeds, p=0.024). Case 4, Molecular Dynamics MD17: ID@100 ADE is 0.0285 versus ESTAG 0.1467; OOD@100 is 0.0316 versus 0.1411 (single seed). For each case, we present the objective, applied SKG theory, parameter settings, baseline comparison protocol, data results, and sources of advantage. Following the cases, we provide the complete methodology: pre-validation, task invariant construction, three-stage training, residual training, and the four theorems and one proposition supporting these methods. This paper not only demonstrates effective configurations of SKG across four domains but also honestly reports the variance of single-run experiments, limitations of single-seed results, negative updates caused by parameterization mismatch, and practical experience of using engineering thresholds as diagnostic signals rather than hard constraints.

Jian An, Chaoshi Wu, Xinpan Luo

Scientific ML OOD Generalization Cross-Domain Generalization Invariant Representation Learning

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Mar 20, 2026

From Data to Laws: Neural Discovery of Conservation Laws Without False Positives

Conservation laws are fundamental to understanding dynamical systems, but discovering them from data remains challenging due to parameter variation, non-polynomial invariants, local minima, and false positives on chaotic systems. We introduce NGCG, a neural-symbolic pipeline that decouples dynamics learning from invariant discovery and systematically addresses these challenges. A multi-restart variance minimiser learns a near-constant latent representation; system-specific symbolic extraction (polynomial Lasso, log-basis Lasso, explicit PDE candidates, and PySR) yields closed-form expressions; a strict constancy gate and diversity filter eliminate spurious laws. On a benchmark of nine diverse systems including Hamiltonian and dissipative ODEs, chaos, and PDEs, NGCG achieves consistent discovery (DR=1.0, FDR=0.0, F1=1.0) on all four systems with true conservation laws, with constancy two to three orders of magnitude lower than the best baseline. It is the only method that succeeds on the Lotka--Volterra system, and it correctly outputs no law on all five systems without invariants. Extensive experiments demonstrate robustness to noise (

σ= 0.1

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Rahul D Ray

Department of Electronics and Electrical Engineering, BITS Pilani, Hyderabad Campus

Scientific Discovery Dynamical Systems Neuro-Symbolic Reasoning

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Jul 7, 2026

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension

We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations. Our main theoretical contribution is an explicit budget allocation condition relating the number

N

of training pairs, the number

n

of input observations, and the output resolution

m

. The condition is derived from a coupled error analysis that interprets the surrogate as a reconstruction from approximate data. This yields a decomposition of the total error into reconstruction and learning contributions that can be analyzed independently. As a consequence, we obtain quantitative scaling laws describing how

N

n

, and

m

must be coupled to guarantee convergence and to balance offline learning and online reconstruction errors. The resulting estimates extend previous analyses of kernel-based operator learning. We further introduce a physics-informed extension that incorporates knowledge of the underlying PDE at evaluation time. Rather than encoding constraints directly into the kernel, we augment the online reconstruction step by penalizing PDE residuals at collocation points. The method requires no retraining for new inputs. Numerical experiments illustrate the theoretical findings and demonstrate the effectiveness of the proposed physics-informed reconstruction strategy.

Rüdiger Kempf

Applied and Numerical Analysis University of Bayreuth 95440 Bayreuth, Germany

Kernel Methods PDE Operator Learning Operator Learning

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