Papers
Machine learning for physics, as it is published.
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
Papers
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
7,943 papers · newest first
cs.RO
Rigid-body motion planning is fundamental to robotic transport and manipulation, where both object position and orientation determine whether a body can move through cluttered environments. This coupling makes planning chal- lenging because translation and rotation can be constrained very differently by surrounding geometry. We propose Shape- Aware Neural Time Fields, a physics-informed neural motion planning framework that learns a reusable travel-time, or cost- to-go, representation for rigid-body motion while explicitly accounting for these distinct geometric restrictions. The learned field captures local motion difficulty in translation and rotation and is paired with a sampling-based planner that balances progress toward the goal with the cost of reaching nearby poses. We evaluate the framework across 2D and 3D rigid- body planning tasks and non-prehensile manipulation through object pushing in diverse environments. Results show substantial improvements in planning success and inference efficiency over physics-informed neural planning baselines, while remaining competitive with classical sampling-based planners at significantly lower planning times. Ablation studies further validate the contributions of both the learned representation and the proposed planning strategy. Finally, closed-loop pushing experiments under execution deviations and external disturbances demonstrate that fast replanning enables reactive and adaptive task execution.
physics.flu-dyn
Reconstructing flow fields from sparse and noisy measurements becomes particularly challenging when data are completely absent from dynamically critical regions, such as the vortex-formation region of a wake. Conventional interpolation and numerical reconstruction methods generally require sufficient spatial or boundary information, while physics-informed neural networks (PINNs) can also face difficulties when sparse and noisy observations provide little or no supervision in the region of interest. To address this gap, we propose a Fourier-feature-embedded complex-valued physics-informed convolutional residual network (FCV-PICRN) for sparse, gappy, and noisy flow-field reconstruction. The framework integrates Fourier features for oscillatory and multiscale structures, complex-valued representations for coupled amplitude–phase learning, and convolutional residual blocks constrained by the Navier–Stokes equations. The method is first verified using the Taylor–Green vortex at and then evaluated for the cylinder wake at . Three severe missing-data configurations are imposed in the dynamically sensitive wake: a large hole, a large truncation, and a plus-shaped gap extending in both streamwise and transverse directions. These gaps are further combined with additive Gaussian and multiplicative speckle noise. Despite having no supervised velocity data inside the excluded regions, FCV-PICRN reconstructs velocity, pressure, and vorticity with high structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR), and remains robust under Gaussian noise up to . Finally, for forced two-dimensional Kolmogorov turbulence with Gaussian noise, FCV-PICRN yields lower reconstruction errors than a conventional PINN. These results demonstrate robust physics-informed reconstruction of severely incomplete and noisy flows across laminar and turbulent regimes.
cs.LG
The Long-Range Ising Model benchmark (LRIM) guarantees long-range dependence by construction: each label is the node's spin times the spin field convolved with a power-law coupling, so any model's distance from the target is measurable. We prove that a readout whose filter is a polynomial in the adjacency, the linear core of isotropic message passing and spectral graph networks, leaves an error floor that no degree lowers, because the target varies along a level set of the spectrum on which every such filter is constant. Computed exactly, the floor and the best filter of each degree predict two spectral networks adapted from published architectures to within a tenth of a decade. A filter escapes the floor only if it weighs separately the offsets the adjacency lumps together, and must still resolve the coupling across the whole lattice. A strided filter of about fifty coefficients does both: fitted to the training labels, its test error is 52 times below the best published network's. A dilated convolutional network beats the best published result at 256 nodes, matches it at 1,024, and gives the first in-domain results at the three larger sizes, while a Fourier neural operator with its standard modes falls further behind as the lattice grows. At its standard budget the dilated network stays two to four orders of magnitude short of a larger strided filter fitted to the labels. The analysis carries over to the benchmark's second coupling.
cs.LG
Physics-informed neural networks (PINNs) reduce or eliminate the need for large labelled datasets by enforcing governing equations during training. Physics-informed Deep Operator Networks (PI-DeepONets) extend this approach to learning solution operators, enabling rapid prediction across families of problems. Despite these advantages, we show that their application to higher-dimensional problems remains limited by the computational cost of training. To address this issue, we propose a modified PI-DeepONet architecture that reduces this cost by removing redundancy in how the Branch network processes input functions across collocation points. The proposed formulation is mathematically equivalent to the original architecture but reduces input tensor sizes and the number of Branch network evaluations. We analyse the computational complexity of both architectures and derive theoretical scaling laws for training time with respect to the number of collocation points and input functions. The proposed architecture is evaluated on 1D, 2D, and 3D linear advection problems. In all cases, it achieves comparable predictive accuracy to the original PI-DeepONet while consistently reducing training time. In 2D experiments, a maximum speed-up of is observed, with empirical training-time scaling agreeing with the predicted linear dependence on collocation points and input functions. Furthermore, training a 3D model on an NVIDIA A100 GPU is only feasible using the proposed architecture, as the original formulation exceeds memory limits. These results demonstrate that careful consideration of how PI-DeepONets are implemented can yield substantial gains, enhancing the practical performance of PI-DeepONets and enabling their application to otherwise intractable physics-informed learning problems.
cs.LG
Genetic and drug perturbation screens are important tools for elucidating disease mechanisms and validating therapeutic targets, but experimental costs limit the number of candidates that can be tested. Existing perturbation screening methods typically update the surrogate model with feedback while keeping the acquisition function fixed, limiting their ability to adapt selection to different response landscapes. Experimental feedback reveals current hits and informs subsequent selection by updating candidate predictions, providing a training signal for learning how to select experiments. We formulate budgeted perturbation discovery as a sequential decision problem and propose Temporal Difference Active Learning (TDAL), which learns an acquisition function online through temporal difference learning from a single screening trajectory, accounting for current hits and future discoveries. TDAL uses the Hellinger distance between hit probabilities for unmeasured candidates before and after an experiment to weight successor value, and reuses measured outcomes through leave-batch-out (LBO) to construct virtual transitions and alleviate training data scarcity. Across eight public screens spanning single, double, and triple perturbations under varied experimental configurations, TDAL achieves an average rank of 1.63 among eleven methods and ranks first on four tasks, demonstrating its adaptability across response landscapes.
cs.AI
Neural operators approximate solution operators of partial differential equations at a fraction of the cost of numerical solvers. Efficient grid-based architectures such as the Fourier neural operator (FNO) assume uniform rectangular grids, whereas engineering simulations use large, irregular, and locally refined meshes. We introduce L-SplineFNO, a memory-efficient neural operator that couples an FNO backbone with a sparse, learnable tensor-product B-spline transfer between unstructured meshes and a latent Cartesian grid. A local normalised scatter avoids the geometry-dependent solve of analytic spline transformation while preserving compact support, partition of unity, and spline smoothness by construction. The neural operator, conditioned on global design and operating parameters, learns the mapping of geometry to the field solution. Across six three-dimensional engineering benchmarks, L-SplineFNO achieves strong predictive accuracy while requiring substantially less memory and compute than baseline operators, scaling to 26.6 million nodes in training and 46 million in inference on a single A100 GPU. It also supports zero-shot super-resolution and efficient closed-form spatial derivatives. Uniquely, the analytic spline decoder yields rigorous prediction bounds over continuous space and uncertain parameters, via Bernstein convex hulls and Taylor models, demonstrated on a 29.2-million-node MAST-U tokamak model.
cs.LG
Physics-informed Gaussian processes (GPs) provide a principled framework for scientific inference by expressing uncertainty over empirical measurements, boundary conditions, and governing equations. However, they struggle to scale to larger datasets and nonlinear information. Conversely, diffusion models excel at learning complex distributions over functions from massive datasets, but struggle in scientific contexts where training data are scarce and physical or observational information must be incorporated. We propose a structured posterior-correction framework that combines a tractable Gaussian reference with data-driven corrections via generative learning. After a mean correction and covariance calibration, a diffusion model learns a targeted correction in a low-dimensional subspace selected to capture discrepancies from the reference, while the complement retains its Gaussian law. Across three scientific inference tasks, these corrections recover hidden modes, improve sample structure, and reduce prediction error relative to the Gaussian reference. Comparisons with full-field generative models reveal task-dependent benefits and tradeoffs between predictive accuracy and computational cost.
physics.comp-ph
Morphodynamic simulations require repeated coupling between hydrodynamic solvers, sediment transport modules, and bed updating. For long duration, multi-scenario simulations on large unstructured meshes, such coupling is computationally demanding. This study proposes an Adaptive-Horizon Graph Neural Operator (AH-GNO) that formulates bed evolution as a graph operator learning problem from recent hydrodynamic and topographic states to predict future bed elevation increments. The model operates directly on the native unstructured meshes. The approach integrates area-weighted graph learning, historical state selection, and forecast horizon estimation, allowing the effective history length (K) and update interval (B) to vary with the evolving flow and bed state. Using Telemac2D/GAIA solutions as supervised numerical references, the framework is evaluated on the official Bump and Yen bend benchmarks and on a field-scale application (Waiho River, New Zealand). Results show that the AH-GNO reproduces the main patterns of bedform migration, bend-scale erosion and deposition, and localized bed adjustment. Across the three cases, the tested CPU-GPU deployment reduced post-training bed-update workflow time from 12~1204 s with GAIA to 0.08~3.34 s with AH-GNO. This improvement corresponds to deployment-specific accelerations of approximately 150~360 times relative to 4-core GAIA CPU configurations, and with 105~186 times gains for 20-core CPU configurations. These results suggest that, while retaining hydrodynamic feedback from TELEMAC-2D, a learned operator for bed updating can provide an efficient acceleration component for morphodynamic scenario analysis and rapid coupled simulation.
cs.LG
Neural PDE solvers commonly generate multi-step predictions through autoregressive rollout, recursively applying a learned evolution operator and feeding each prediction back as input for the next step. Approximation errors can therefore propagate through the rollout, causing predictions at a shared target time to depend on their temporal origins and rollout depths. For a well-posed deterministic PDE flow, however, states at different times along the same physical trajectory should, under exact evolution, reach the same target state. To this end, we propose Align Latent Rollout (ALR), a regularization approach that promotes consistency across rollout origins through the neural PDE solver's internal representations. A second-order Taylor analysis of latent discrepancy propagation motivates two objectives: zeroth-order latent state consistency, which aligns representations at a shared target time, and first-order latent dynamics consistency, which aligns local evolution responses to shared perturbations. ALR can be integrated into different neural PDE solvers by regularizing suitable internal representations, without modifying their backbone architectures. Experiments across multiple PDE benchmarks and neural-operator backbones show that ALR improves prediction accuracy while reducing shared-target discrepancies across rollout origins.
cs.LG
Accurate medium- to long-range epidemic forecasting requires extrapolating high-dimensional, heterogeneous and nonstationary dynamics from partial observations. Yet hybrid models often leave implicit which observations inform which epidemic processes and how learned graph interactions modify system state. We introduce LE-EpiGNODE, which replaces generic message passing with process-specific, mechanism-guided neural operators: age-contact information drives Lagrangian infection generation, whereas mobility drives conservative Eulerian population transport within a structure-preserving universal differential equation. We evaluated LE-EpiGNODE across 14 controlled synthetic mechanisms spanning time-modulated, state-dependent, nonlinear and coupled dynamics, three complementary COVID-19 settings, 21 comparator models and five targeted ablations. Forecasting gains tended to become more pronounced at longer horizons; at the longest horizon, LE-EpiGNODE achieved the lowest WMAPE in all three real-world datasets, reducing error by 17.7-40.0% relative to the best baseline. Controlled ablations linked these gains to the Lagrangian-Eulerian decomposition and process-aligned priors, while synthetic ground truth showed that learned operators and induced state fluxes track known generating dynamics. These results support mechanism-organized graph neural dynamics as a route to reliable long-horizon extrapolation with directly testable, process-level mechanistic interpretation beyond trajectory accuracy.
physics.comp-ph
Sharp-interface immersed boundary methods provide a versatile framework for simulating flows with complex moving boundaries, but their irregular data structures, dynamic sparsity, and discontinuous pressure operators present significant challenges for efficient multi-GPU implementation. This work presents a fully GPU-native, multi-GPU acceleration of the sharp-interface immersed boundary solver, ViCar3D. The implementation combines a hybrid OpenACC/CUDA programming model with a matrix decomposition that isolates dynamically changing immersed-boundary operators, GPU-optimized geometric kernels, asynchronous dual-stream sparse matrix–vector execution, and a symmetric-memory-based sparse communication strategy. A GPU-oriented iterative solver employing a preconditioned stabilized bi-conjugate gradient (BiCGStab) method is developed to efficiently treat the pressure Poisson equation on highly stretched Cartesian grids. The resulting framework preserves the accuracy and versatility of the original solver while delivering substantial acceleration and scalability for simulations involving complex moving and deforming immersed boundaries, thereby extending the applicability of sharp-interface immersed boundary methods to extreme-scale computational fluid dynamics.
cs.LG
Current approaches for steady partial differential equations surrogate models on unstructured meshes apply a single mixing mechanism to the whole solution. This paper proposes an architecture that partitions the solution among vanilla transformer experts, each focused on a different spectral scale. The partition is built from a discrete Hodge Laplacian , that serves as a fitting layer measuring high-frequency content. A gating mechanism takes the mesh as input and produces the per-vertex weights that recombine the expert outputs. AirFRANS is a steady Reynolds-averaged Navier–Stokes (RANS) airfoil benchmark. We evaluate our approach in a reduced remeshed version of the benchmark with each unstructured mesh counting 9.6K faces and 4.9K vertices. We compare our approach with the Transolver on the same dataset and dataset slit. Our approach reduces relative error by 31% and interior mean squared error by 47%.
cs.LG
Neural emulation need not require learning a substitute for known physics. We investigate PolyNets that couple a continuous-time neural representation of polynomial dynamics with a simple recurrent network for discrete-time integration. When the governing coefficients are known, the resulting tensor graph requires no training and preserves the prescribed numerical scheme while enabling efficient hardware execution and parallel simulation. Using the one-dimensional Korteweg-de Vries equation, we compare PolyNet with CPU and GPU finite-difference Runge-Kutta solvers and three trained neural models: a state-map emulator, a physics-informed predictor, and a learned-tendency integrator. Analytical soliton solutions provide a reference for amplitude and phase errors across grid resolutions, 10^6 dispersively scaled time steps, ensembles of up to 10^4 trajectories, and varying initial amplitudes. PolyNet achieves accuracy comparable to the numerical solvers, including at amplitudes outside the learned models' training conditions. It combines this fidelity with high GPU throughput, approximately constant over the tested resolution range, and favorable ensemble scaling.
physics.flu-dyn
Lab-scale membrane distillation (MD) modules are commonly used for membrane characterization and developing empirical heat-transfer correlations. Entrance-induced flow structures can introduce geometry-specific effects into measured temperature polarization (TP) and heat transfer. However, the dependence of these effects on module geometry and flow condition remains unclear. We performed three-dimensional computational fluid dynamics (CFD) simulations of direct contact membrane distillation (DCMD) over inlet Reynolds numbers of -, focusing on side-chamber length and main-channel height. We discovered that counter-rotating streamwise vortices formed near the main-channel entrance across all geometries, but their downstream persistence increased with . At lower , the vortices mostly decayed before mid-channel, while at higher they persisted farther downstream and produced pronounced spatial variations in TP. Increasing side-chamber length reduced the secondary-flow kinetic energy entering the main channel, and generally strengthened TP, whereas increasing main-channel height reduced the bulk velocity and streamwise kinetic energy, resulting in a thicker thermal boundary layer and stronger TP. For most geometries, the deviation from the straight-channel baseline changed from stronger TP at lower to weaker TP at higher . Entrance effects therefore vary in both magnitude and direction with operating condition and cannot be represented by a constant correction across the Reynolds-number range.
cs.SD
Head-related transfer function (HRTF) spatial upsampling from sparse measurements is a fundamental challenge in personalized binaural audio. We formulate HRTF upsampling as an operator learning problem and introduce SPARO, a neural operator that maps sparse measurements at a set of spatial directions to the HRTF field, a continuous representation that can be queried at arbitrary positions. SPARO projects the measurements onto a learned set of spherical latent modes, processes the latent modes with Transformer blocks, and decodes the resulting representations at query directions. On SONICOM, using the LAP24 measurement configuration, SPARO attains the best log-spectral distortion (LSD) and interaural level difference (ILD) error at every sparsity level from 3 to 100 measurements (18% lower LSD and 43% lower ILD error than the strongest baseline at 100 measurements) while remaining competitive in interaural time difference (ITD) error. It reconstructs a dense HRTF 15 to 373 times faster than the leading neural-field method RANF. We further validate the approach on HUTUBS, demonstrating its effectiveness across HRTF datasets.
cs.LG
Neural operators learn mappings between function spaces, enabling fast surrogate solutions to partial differential equations. Despite remarkable architectural diversity, these methods often share a common input representation: raw coordinate-value pairs . We ask whether inputs aligned with PDE differential structure can improve learning. Through Picard iteration on mild solutions, we show that derivatives of the input appear explicitly in the solution operator, suggesting that providing derivative features should reduce the network's implicit differentiation burden. We prove this intuition: providing derivative features improves approximation bounds from to , where is parameter count, is input regularity, is the PDE order, and is spatial dimension. Our central finding, however, is a surprise: the optimal derivative order is strictly less than the PDE order . This gap arises from a bias-variance tradeoff in spectral space that we characterize in closed form. Learning from data achieves automatic spectral regularization. We introduce -NO (del-NO), for derivative-augmented neural operators, an architecture-agnostic augmentation that provides learnable fractional derivative features to any neural operator backbone. Across benchmark problems and architectures, -NO consistently improves prediction accuracy, with learned orders that reflect a representation of known physics modulated by noise and finite-sample constraints.
cs.LG
We present several advances on neural operators by viewing the action of operator layers as the minimizers of Bregman regularized optimization problems over Banach function spaces. The proposed framework allows interpreting the activation operators as Bregman proximity operators from dual to primal space. This novel viewpoint is general enough to recover classical neural operators as well as a new variant, coined Bregman neural operators, which includes the inverse activation operator and features the same expressivity of standard neural operators. Numerical experiments support the added benefits of the Bregman variant of Fourier neural operators for training deeper and more accurate models.
cs.LG
A staged physics-informed neural network (PINN) is proposed for identifying the inductance, capacitance and parasitic resistances of a DC buck converter from time-domain data. Gradients are released in the order of L to C to rL to rC, a sequence derived from sensitivity analysis. The five-stage schedule recovers L and C to within 5% and the series ESR to 10%, while a three-stage variant attains the same accuracy 11% faster. An 84 factorial sweep confirms that the trained PINN remains accurate for simultaneous 8% perturbations of all four components, achieving a waveform RMSE of 2.6 x 10-2 over 5 ms-an order-of-magnitude better than a simultaneous-training baseline.
cs.IT
Digital-domain self-interference cancellation is essential in in-band full-duplex radios after passive suppression and analog cancellation. It is particularly challenging when the desired signal is strong relative to the residual self-interference. In this regime, conventional iterative digital cancellers update their coefficients from desired-signal-contaminated received samples and may suffer substantial performance degradation. This paper reformulates digital-domain self-interference cancellation as an operator-learning problem. The proposed framework learns the temporal evolution of the residual self-interference channel from historical observations and uses the learned operator together with the known local transmit signal to reconstruct the current residual self-interference. A Transformer neural operator is used to realize this framework. The resulting method is trained in a desired-signal-free setting and then applied in the presence of a desired signal. A continuity-based analysis characterizes the sensitivity of the learned operator to the resulting input perturbation. Numerical experiments in static and time-varying channels, including time-varying SIR conditions, demonstrate stable cancellation performance over a wide range of interference levels. At 30 dB SIR, the proposed method improves the cancellation performance by 5–15 dB over the considered conventional methods.
cs.LG
Physics-informed neural networks provide a flexible framework for learning parametric PDE solution families without labeled data, yet preserving accurate derivatives across heterogeneous regimes remains challenging. Structured neural solvers offer compact representations, but restrictive conditional parameterizations can limit adaptation across the solution family. We introduce BeTINN, a structured conditional architecture extending time-induced modulation through multi-directional time-parameter conditioning and a joint residual pathway. We evaluate BeTINN on the Heston stochastic-volatility PDE, a demanding parametric problem with mixed derivatives and economically relevant first- and second-order sensitivities. BeTINN improves joint accuracy across normalized option value and key sensitivity metrics relative to our baselines. Controlled ablations characterize the roles of its architectural components. We further find that validation physics loss is informative but does not fully determine differential fidelity, and that accurate solution values can coexist with localized derivative errors. These results support structured conditional adaptation and motivate derivative-aware evaluation when sensitivities are downstream quantities of interest.