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Georgia Tech Research Institute

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Selected work

Representative Papers

Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment

Jun 23, 2026

This work addresses the redundancy of complex Fourier bases in neural operators when learning solution operators for real-valued partial differential equations (PDEs). The authors propose the Hartley Neural Operator (HNO), which replaces the complex-valued FFT in Fourier Neural Operators (FNOs) with a purely real discrete Hartley transform, adaptively selecting the optimal spectral basis according to the symmetry and phase characteristics of the underlying PDE operator while maintaining the same number of parameters. They establish, for the first time, a theoretical link between spectral basis choice and the symmetry of Green’s functions, and formulate a guideline for selecting real or complex spectral bases based on operator type—elliptic versus time-dependent. Experiments demonstrate that HNO significantly outperforms FNO on self-adjoint elliptic problems such as Poisson’s equation, whereas FNO excels in phase-sensitive dynamic problems like wave propagation and Navier–Stokes, with performance differences monotonically correlated with the operator’s phase content.

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GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators

Jun 06, 2026

This work addresses the challenge that existing neural operators struggle to simultaneously satisfy energy conservation and entropy production structures dictated by nonequilibrium thermodynamics in function space. The authors embed the full GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework into a Fourier neural operator, learning energy and entropy functionals while parameterizing Poisson and friction operators via diagonal Fourier multipliers combined with rank-one projections to rigorously enforce thermodynamic degeneracy conditions. This approach is the first to guarantee thermodynamic consistency at machine precision in function space without requiring penalty terms or post-processing. Additionally, it introduces a gauge-invariant dissipation diagnostic to disentangle reversible and dissipative dynamics. On 1D and 2D problems, the model achieves zero-shot structural fidelity at 4× super-resolution, accurately recovers the physical dissipation hierarchy, and matches or outperforms existing unconstrained and energy-penalized baselines.

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Recent publications

Latest Papers

Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment

Jun 23, 2026

This work addresses the redundancy of complex Fourier bases in neural operators when learning solution operators for real-valued partial differential equations (PDEs). The authors propose the Hartley Neural Operator (HNO), which replaces the complex-valued FFT in Fourier Neural Operators (FNOs) with a purely real discrete Hartley transform, adaptively selecting the optimal spectral basis according to the symmetry and phase characteristics of the underlying PDE operator while maintaining the same number of parameters. They establish, for the first time, a theoretical link between spectral basis choice and the symmetry of Green’s functions, and formulate a guideline for selecting real or complex spectral bases based on operator type—elliptic versus time-dependent. Experiments demonstrate that HNO significantly outperforms FNO on self-adjoint elliptic problems such as Poisson’s equation, whereas FNO excels in phase-sensitive dynamic problems like wave propagation and Navier–Stokes, with performance differences monotonically correlated with the operator’s phase content.

0 citationsRead paper

GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators

Jun 06, 2026

This work addresses the challenge that existing neural operators struggle to simultaneously satisfy energy conservation and entropy production structures dictated by nonequilibrium thermodynamics in function space. The authors embed the full GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework into a Fourier neural operator, learning energy and entropy functionals while parameterizing Poisson and friction operators via diagonal Fourier multipliers combined with rank-one projections to rigorously enforce thermodynamic degeneracy conditions. This approach is the first to guarantee thermodynamic consistency at machine precision in function space without requiring penalty terms or post-processing. Additionally, it introduces a gauge-invariant dissipation diagnostic to disentangle reversible and dissipative dynamics. On 1D and 2D problems, the model achieves zero-shot structural fidelity at 4× super-resolution, accurately recovers the physical dissipation hierarchy, and matches or outperforms existing unconstrained and energy-penalized baselines.

0 citationsRead paper