{ "scope": "Short software correctness checks; not paper accuracy reproduction or convergence evidence.", "torch": "2.14.1+cu130", "device": "cpu", "gpu": null, "paper": "https://arxiv.org/abs/2308.08468v1", "cases": { "expert_allen_cahn": { "label": "Allen\u2013Cahn \u00b7 1D + time", "configuration": { "shape": "SpaceTime1D", "x_min": -1.0, "x_max": 1.0, "y_min": 0.0, "y_max": 1.0, "t_min": 0.0, "t_max": 1.0, "cylinder_x": 0.2, "cylinder_y": 0.2, "cylinder_radius": 0.05, "fourth_order": 0.00152587890625, "startup_time": 0.1, "points": 32, "boundary_points": 4, "adaptive_sampling": {}, "sampling": "random", "seed": 7, "source": 5.0, "layers": [ 16, 16 ], "iterations": 10, "lr": 0.001, "device": "cpu", "loss_formulation": "mean", "pde_weight": 1.0, "boundary_weight": 1.0, "bc_types": { "left": "Dirichlet", "right": "Dirichlet", "bottom": "Dirichlet", "top": "Dirichlet" }, "bc_values": { "left": 0.0, "right": 0.0, "bottom": 0.0, "top": 0.0 }, "boundary_sampling": {}, "pde_expression": "", "bc_targets": {}, "bc_operators": {}, "interior_data": {}, "boundary_data": {}, "network_seed": 7, "method": "expert", "expert_settings": { "chunks": 4, "causal_epsilon": 1.0, "balance_every": 2, "momentum": 0.9, "decay_rate": 0.9, "decay_steps": 2000, "gradient_floor": 1e-12, "weight_cap": 1000000.0 }, "physics": "paper_case", "viscosity": 0.0001, "flow_residuals": [ "u*D(u,x)+v*D(u,y)+D(p,x)-nu*laplace(u)", "u*D(v,x)+v*D(v,y)+D(p,y)-nu*laplace(v)", "D(u,x)+D(v,y)" ], "flow_boundary": { "left": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "right": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "bottom": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "top": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } } }, "pressure_point": [ 0.0, 0.0 ], "pressure_value": 0.0, "pressure_weight": 1.0, "pde_preset": "expert_allen_cahn", "pde_forcing": "0", "sa_lr": 0.005, "sa_initial": 1.0, "sa_max": 1000.0, "sa_boundary": false, "lra_alpha": 0.9, "lra_interval": 10, "lra_epsilon": 1e-12, "lra_max": 1000000.0, "network_type": "fourier", "network_options": { "encoding": "gaussian", "features": 4, "scale": 0.15915494309189535, "weight_factorization": true, "factor_mean": 1.0, "factor_std": 0.1 } }, "interior_count": 32, "constraint_counts": { "initial": 4, "periodic_x": 4 }, "fields": [ "u" ], "coordinates": [ "x", "t" ], "steps": 10, "initial_losses": { "pde": 0.40546637773513794, "initial": 0.09463468939065933, "periodic_x": 0.07750140130519867, "total": 0.49153444170951843 }, "final_losses": { "pde": 0.28475576639175415, "initial": 0.12060952931642532, "periodic_x": 0.043480969965457916, "total": 1.4312503337860107 }, "checkpoint_resume_identical": true }, "expert_advection": { "label": "Advection \u00b7 1D + time", "configuration": { "shape": "SpaceTime1D", "x_min": 0.0, "x_max": 6.283185307179586, "y_min": 0.0, "y_max": 1.0, "t_min": 0.0, "t_max": 1.0, "cylinder_x": 0.2, "cylinder_y": 0.2, "cylinder_radius": 0.05, "fourth_order": 0.00152587890625, "startup_time": 0.1, "points": 32, "boundary_points": 4, "adaptive_sampling": {}, "sampling": "random", "seed": 7, "source": 50.0, "layers": [ 16, 16 ], "iterations": 10, "lr": 0.001, "device": "cpu", "loss_formulation": "mean", "pde_weight": 1.0, "boundary_weight": 1.0, "bc_types": { "left": "Dirichlet", "right": "Dirichlet", "bottom": "Dirichlet", "top": "Dirichlet" }, "bc_values": { "left": 0.0, "right": 0.0, "bottom": 0.0, "top": 0.0 }, "boundary_sampling": {}, "pde_expression": "", "bc_targets": {}, "bc_operators": {}, "interior_data": {}, "boundary_data": {}, "network_seed": 7, "method": "expert", "expert_settings": { "chunks": 4, "causal_epsilon": 1.0, "balance_every": 2, "momentum": 0.9, "decay_rate": 0.9, "decay_steps": 2000, "gradient_floor": 1e-12, "weight_cap": 1000000.0 }, "physics": "paper_case", "viscosity": 0.01, "flow_residuals": [ "u*D(u,x)+v*D(u,y)+D(p,x)-nu*laplace(u)", "u*D(v,x)+v*D(v,y)+D(p,y)-nu*laplace(v)", "D(u,x)+D(v,y)" ], "flow_boundary": { "left": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "right": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "bottom": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "top": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } } }, "pressure_point": [ 0.0, 0.0 ], "pressure_value": 0.0, "pressure_weight": 1.0, "pde_preset": "expert_advection", "pde_forcing": "0", "sa_lr": 0.005, "sa_initial": 1.0, "sa_max": 1000.0, "sa_boundary": false, "lra_alpha": 0.9, "lra_interval": 10, "lra_epsilon": 1e-12, "lra_max": 1000000.0, "network_type": "fourier", "network_options": { "encoding": "gaussian", "features": 4, "scale": 0.15915494309189535, "weight_factorization": true, "factor_mean": 1.0, "factor_std": 0.1 } }, "interior_count": 32, "constraint_counts": { "initial": 4, "periodic_x": 4 }, "fields": [ "u" ], "coordinates": [ "x", "t" ], "steps": 10, "initial_losses": { "pde": 0.6889663934707642, "initial": 0.7043583989143372, "periodic_x": 0.1374436318874359, "total": 1.1098673343658447 }, "final_losses": { "pde": 0.3011646270751953, "initial": 0.41148048639297485, "periodic_x": 0.01408538967370987, "total": 1.8310176134109497 }, "checkpoint_resume_identical": true }, "expert_stokes": { "label": "Stokes \u00b7 2D channel/cylinder", "configuration": { "shape": "Channel2D", "x_min": 0.0, "x_max": 2.2, "y_min": 0.0, "y_max": 0.41, "t_min": 0.0, "t_max": 1.0, "cylinder_x": 0.2, "cylinder_y": 0.2, "cylinder_radius": 0.05, "fourth_order": 0.00152587890625, "startup_time": 0.1, "points": 32, "boundary_points": 4, "adaptive_sampling": {}, "sampling": "random", "seed": 7, "source": 0.0, "layers": [ 16, 16 ], "iterations": 10, "lr": 0.001, "device": "cpu", "loss_formulation": "mean", "pde_weight": 1.0, "boundary_weight": 1.0, "bc_types": { "left": "Dirichlet", "right": "Dirichlet", "bottom": "Dirichlet", "top": "Dirichlet" }, "bc_values": { "left": 0.3, "right": 0.0, "bottom": 0.0, "top": 0.0 }, "boundary_sampling": {}, "pde_expression": "", "bc_targets": {}, "bc_operators": {}, "interior_data": {}, "boundary_data": {}, "network_seed": 7, "method": "expert", "expert_settings": { "chunks": 4, "causal_epsilon": 1.0, "balance_every": 2, "momentum": 0.9, "decay_rate": 0.9, "decay_steps": 2000, "gradient_floor": 1e-12, "weight_cap": 1000000.0 }, "physics": "paper_case", "viscosity": 0.001, "flow_residuals": [ "u*D(u,x)+v*D(u,y)+D(p,x)-nu*laplace(u)", "u*D(v,x)+v*D(v,y)+D(p,y)-nu*laplace(v)", "D(u,x)+D(v,y)" ], "flow_boundary": { "left": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "right": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "bottom": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "top": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } } }, "pressure_point": [ 0.0, 0.0 ], "pressure_value": 0.0, "pressure_weight": 1.0, "pde_preset": "expert_stokes", "pde_forcing": "0", "sa_lr": 0.005, "sa_initial": 1.0, "sa_max": 1000.0, "sa_boundary": false, "lra_alpha": 0.9, "lra_interval": 10, "lra_epsilon": 1e-12, "lra_max": 1000000.0, "network_type": "fourier", "network_options": { "encoding": "gaussian", "features": 4, "scale": 0.15915494309189535, "weight_factorization": true, "factor_mean": 1.0, "factor_std": 0.1 } }, "interior_count": 32, "constraint_counts": { "inlet": 4, "outlet_traction": 4, "walls": 8, "cylinder": 4 }, "fields": [ "u", "v", "p" ], "coordinates": [ "x", "y" ], "steps": 10, "initial_losses": { "pde": 0.7252090573310852, "inlet": 0.1515892595052719, "outlet_traction": 0.23795665800571442, "walls": 0.12480711191892624, "cylinder": 0.17394936084747314, "total": 0.8972846269607544 }, "final_losses": { "pde": 0.09509105235338211, "inlet": 0.035398148000240326, "outlet_traction": 0.03349527344107628, "walls": 0.02738591656088829, "cylinder": 0.03344890847802162, "total": 0.19326350092887878 }, "checkpoint_resume_identical": true }, "expert_ks": { "label": "Kuramoto\u2013Sivashinsky \u00b7 1D + time", "configuration": { "shape": "SpaceTime1D", "x_min": 0.0, "x_max": 6.283185307179586, "y_min": 0.0, "y_max": 1.0, "t_min": 0.0, "t_max": 1.0, "cylinder_x": 0.2, "cylinder_y": 0.2, "cylinder_radius": 0.05, "fourth_order": 0.00152587890625, "startup_time": 0.1, "points": 32, "boundary_points": 4, "adaptive_sampling": {}, "sampling": "random", "seed": 7, "source": 6.25, "layers": [ 16, 16 ], "iterations": 10, "lr": 0.001, "device": "cpu", "loss_formulation": "mean", "pde_weight": 1.0, "boundary_weight": 1.0, "bc_types": { "left": "Dirichlet", "right": "Dirichlet", "bottom": "Dirichlet", "top": "Dirichlet" }, "bc_values": { "left": 0.0, "right": 0.0, "bottom": 0.0, "top": 0.0 }, "boundary_sampling": {}, "pde_expression": "", "bc_targets": {}, "bc_operators": {}, "interior_data": {}, "boundary_data": {}, "network_seed": 7, "method": "expert", "expert_settings": { "chunks": 4, "causal_epsilon": 1.0, "balance_every": 2, "momentum": 0.9, "decay_rate": 0.9, "decay_steps": 2000, "gradient_floor": 1e-12, "weight_cap": 1000000.0 }, "physics": "paper_case", "viscosity": 0.390625, "flow_residuals": [ "u*D(u,x)+v*D(u,y)+D(p,x)-nu*laplace(u)", "u*D(v,x)+v*D(v,y)+D(p,y)-nu*laplace(v)", "D(u,x)+D(v,y)" ], "flow_boundary": { "left": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "right": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "bottom": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "top": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } } }, "pressure_point": [ 0.0, 0.0 ], "pressure_value": 0.0, "pressure_weight": 1.0, "pde_preset": "expert_ks", "pde_forcing": "0", "sa_lr": 0.005, "sa_initial": 1.0, "sa_max": 1000.0, "sa_boundary": false, "lra_alpha": 0.9, "lra_interval": 10, "lra_epsilon": 1e-12, "lra_max": 1000000.0, "network_type": "fourier", "network_options": { "encoding": "gaussian", "features": 4, "scale": 0.15915494309189535, "weight_factorization": true, "factor_mean": 1.0, "factor_std": 0.1 } }, "interior_count": 32, "constraint_counts": { "initial": 4, "periodic_x": 4 }, "fields": [ "u" ], "coordinates": [ "x", "t" ], "steps": 10, "initial_losses": { "pde": 0.3153444528579712, "initial": 0.6999966502189636, "periodic_x": 0.03483053669333458, "total": 0.682758092880249 }, "final_losses": { "pde": 0.03279031440615654, "initial": 0.2143748253583908, "periodic_x": 0.00355714769102633, "total": 0.24065153300762177 }, "checkpoint_resume_identical": true }, "expert_cavity": { "label": "Lid-driven cavity \u00b7 2D \u00b7 Re=3200", "configuration": { "shape": "Rectangle", "x_min": 0.0, "x_max": 1.0, "y_min": 0.0, "y_max": 1.0, "t_min": 0.0, "t_max": 1.0, "cylinder_x": 0.2, "cylinder_y": 0.2, "cylinder_radius": 0.05, "fourth_order": 0.00152587890625, "startup_time": 0.1, "points": 32, "boundary_points": 4, "adaptive_sampling": {}, "sampling": "random", "seed": 7, "source": 0.0, "layers": [ 16, 16 ], "iterations": 10, "lr": 0.001, "device": "cpu", "loss_formulation": "mean", "pde_weight": 1.0, "boundary_weight": 1.0, "bc_types": { "left": "Dirichlet", "right": "Dirichlet", "bottom": "Dirichlet", "top": "Dirichlet" }, "bc_values": { "left": 0.0, "right": 0.0, "bottom": 0.0, "top": 1.0 }, "boundary_sampling": {}, "pde_expression": "", "bc_targets": {}, "bc_operators": {}, "interior_data": {}, "boundary_data": {}, "network_seed": 7, "method": "expert", "expert_settings": { "chunks": 4, "causal_epsilon": 1.0, "balance_every": 2, "momentum": 0.9, "decay_rate": 0.9, "decay_steps": 2000, "gradient_floor": 1e-12, "weight_cap": 1000000.0 }, "physics": "paper_case", "viscosity": 0.0003125, "flow_residuals": [ "u*D(u,x)+v*D(u,y)+D(p,x)-nu*laplace(u)", "u*D(v,x)+v*D(v,y)+D(p,y)-nu*laplace(v)", "D(u,x)+D(v,y)" ], "flow_boundary": { "left": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "right": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "bottom": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "top": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } } }, "pressure_point": [ 0.0, 0.0 ], "pressure_value": 0.0, "pressure_weight": 1.0, "pde_preset": "expert_cavity", "pde_forcing": "0", "sa_lr": 0.005, "sa_initial": 1.0, "sa_max": 1000.0, "sa_boundary": false, "lra_alpha": 0.9, "lra_interval": 10, "lra_epsilon": 1e-12, "lra_max": 1000000.0, "network_type": "fourier", "network_options": { "encoding": "gaussian", "features": 4, "scale": 0.15915494309189535, "weight_factorization": true, "factor_mean": 1.0, "factor_std": 0.1 } }, "interior_count": 32, "constraint_counts": { "lid": 4, "walls": 12, "pressure_gauge": 1 }, "fields": [ "u", "v", "p" ], "coordinates": [ "x", "y" ], "steps": 10, "initial_losses": { "pde": 0.2346537858247757, "lid": 0.5926468372344971, "walls": 0.13969473540782928, "pressure_gauge": 0.02742101065814495, "total": 0.5061886310577393 }, "final_losses": { "pde": 0.03579527139663696, "lid": 0.14701472222805023, "walls": 0.08998772501945496, "pressure_gauge": 0.0011653718538582325, "total": 0.16627237200737 }, "checkpoint_resume_identical": true }, "expert_torus": { "label": "Navier\u2013Stokes torus \u00b7 2D + time \u00b7 Taylor\u2013Green variation", "configuration": { "shape": "SpaceTime2D", "x_min": 0.0, "x_max": 6.283185307179586, "y_min": 0.0, "y_max": 6.283185307179586, "t_min": 0.0, "t_max": 10.0, "cylinder_x": 0.2, "cylinder_y": 0.2, "cylinder_radius": 0.05, "fourth_order": 0.00152587890625, "startup_time": 0.1, "points": 32, "boundary_points": 4, "adaptive_sampling": {}, "sampling": "random", "seed": 7, "source": 0.0, "layers": [ 16, 16 ], "iterations": 10, "lr": 0.001, "device": "cpu", "loss_formulation": "mean", "pde_weight": 1.0, "boundary_weight": 1.0, "bc_types": { "left": "Dirichlet", "right": "Dirichlet", "bottom": "Dirichlet", "top": "Dirichlet" }, "bc_values": { "left": 0.0, "right": 0.0, "bottom": 0.0, "top": 0.0 }, "boundary_sampling": {}, "pde_expression": "", "bc_targets": {}, "bc_operators": {}, "interior_data": {}, "boundary_data": {}, "network_seed": 7, "method": "expert", "expert_settings": { "chunks": 4, "causal_epsilon": 1.0, "balance_every": 2, "momentum": 0.9, "decay_rate": 0.9, "decay_steps": 2000, "gradient_floor": 1e-12, "weight_cap": 1000000.0 }, "physics": "paper_case", "viscosity": 0.01, "flow_residuals": [ "u*D(u,x)+v*D(u,y)+D(p,x)-nu*laplace(u)", "u*D(v,x)+v*D(v,y)+D(p,y)-nu*laplace(v)", "D(u,x)+D(v,y)" ], "flow_boundary": { "left": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "right": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "bottom": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "top": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } } }, "pressure_point": [ 0.0, 0.0 ], "pressure_value": 0.0, "pressure_weight": 1.0, "pde_preset": "expert_torus", "pde_forcing": "0", "sa_lr": 0.005, "sa_initial": 1.0, "sa_max": 1000.0, "sa_boundary": false, "lra_alpha": 0.9, "lra_interval": 10, "lra_epsilon": 1e-12, "lra_max": 1000000.0, "network_type": "fourier", "network_options": { "encoding": "gaussian", "features": 4, "scale": 0.15915494309189535, "weight_factorization": true, "factor_mean": 1.0, "factor_std": 0.1 } }, "interior_count": 32, "constraint_counts": { "initial": 4, "periodic_x": 4, "periodic_y": 4, "mean_velocity": 4 }, "fields": [ "u", "v", "w" ], "coordinates": [ "x", "y", "t" ], "steps": 10, "initial_losses": { "pde": 0.06235682591795921, "initial": 0.19442029297351837, "periodic_x": 0.01110832765698433, "periodic_y": 0.19275003671646118, "mean_velocity": 0.129248708486557, "total": 0.19423866271972656 }, "final_losses": { "pde": 0.005647842772305012, "initial": 0.6577234864234924, "periodic_x": 0.02299049310386181, "periodic_y": 0.022055096924304962, "mean_velocity": 0.010210794396698475, "total": 0.32768765091896057 }, "checkpoint_resume_identical": true }, "expert_cylinder": { "label": "Navier\u2013Stokes cylinder \u00b7 2D + time \u00b7 startup variation", "configuration": { "shape": "ChannelTime2D", "x_min": 0.0, "x_max": 2.2, "y_min": 0.0, "y_max": 0.41, "t_min": 0.0, "t_max": 1.0, "cylinder_x": 0.2, "cylinder_y": 0.2, "cylinder_radius": 0.05, "fourth_order": 0.00152587890625, "startup_time": 0.1, "points": 32, "boundary_points": 4, "adaptive_sampling": {}, "sampling": "random", "seed": 7, "source": 0.0, "layers": [ 16, 16 ], "iterations": 10, "lr": 0.001, "device": "cpu", "loss_formulation": "mean", "pde_weight": 1.0, "boundary_weight": 1.0, "bc_types": { "left": "Dirichlet", "right": "Dirichlet", "bottom": "Dirichlet", "top": "Dirichlet" }, "bc_values": { "left": 1.5, "right": 0.0, "bottom": 0.0, "top": 0.0 }, "boundary_sampling": {}, "pde_expression": "", "bc_targets": {}, "bc_operators": {}, "interior_data": {}, "boundary_data": {}, "network_seed": 7, "method": "expert", "expert_settings": { "chunks": 4, "causal_epsilon": 1.0, "balance_every": 2, "momentum": 0.9, "decay_rate": 0.9, "decay_steps": 2000, "gradient_floor": 1e-12, "weight_cap": 1000000.0 }, "physics": "paper_case", "viscosity": 0.001, "flow_residuals": [ "u*D(u,x)+v*D(u,y)+D(p,x)-nu*laplace(u)", "u*D(v,x)+v*D(v,y)+D(p,y)-nu*laplace(v)", "D(u,x)+D(v,y)" ], "flow_boundary": { "left": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "right": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "bottom": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } }, "top": { "u": { "type": "Dirichlet", "target": "y", "operator": "" }, "v": { "type": "Dirichlet", "target": "0", "operator": "" } } }, "pressure_point": [ 0.0, 0.0 ], "pressure_value": 0.0, "pressure_weight": 1.0, "pde_preset": "expert_cylinder", "pde_forcing": "0", "sa_lr": 0.005, "sa_initial": 1.0, "sa_max": 1000.0, "sa_boundary": false, "lra_alpha": 0.9, "lra_interval": 10, "lra_epsilon": 1e-12, "lra_max": 1000000.0, "network_type": "fourier", "network_options": { "encoding": "gaussian", "features": 4, "scale": 0.15915494309189535, "weight_factorization": true, "factor_mean": 1.0, "factor_std": 0.1 } }, "interior_count": 32, "constraint_counts": { "initial": 4, "inlet": 4, "outlet_traction": 4, "walls": 8, "cylinder": 4 }, "fields": [ "u", "v", "p" ], "coordinates": [ "x", "y", "t" ], "steps": 10, "initial_losses": { "pde": 0.5239555835723877, "initial": 0.043804705142974854, "inlet": 0.47185713052749634, "outlet_traction": 0.06717724353075027, "walls": 0.2738979756832123, "cylinder": 0.0781959667801857, "total": 0.7109421491622925 }, "final_losses": { "pde": 0.06893320381641388, "initial": 0.04836221784353256, "inlet": 0.4146049916744232, "outlet_traction": 0.02691071294248104, "walls": 0.0392855741083622, "cylinder": 0.04522354155778885, "total": 0.47635775804519653 }, "checkpoint_resume_identical": true } } }