Inclusion Criteria:  Adults (age 21-80) who meet clinical signs and symptoms of heart failure based on clinical assessment. The subject must meet at least one of the following hemodynamic criteria for HFpEF of PH-HFpEF by right heart catheterization (RHC) within 6 months of screening visit;  A) HFpEF:  At rest: mean pulmonary artery occlusions pressure (PAOP) > 15, pulmonary vascular resistance (PVR) < 3 Wood Units, or HFpEF with fluid challenge, defined as increase in PAOP post 500 cc fluid bolus: mean PAOP > 18, PVR < 3 Wood Units, or HFpEF with exercise, defined as peak mean PAOP > 17, PVR < 3 Wood Units if age < 50 or peak mean PAOP > 19 and PVR < 3 Wood Units if age >= 50  B) PH-HFpEF:  At rest: mean pulmonary artery occlusion pressure (PAOP) > 15, mean pulmonary artery pressure (PAP) >= 25, pulmonary vascular resistance (PVR) > 3 Wood Units, or PH-HFpEF with fluid challenge, defined as increase in PAOP post 500 cc fluid bolus: mean PAOP > 18, mean PAP >= 25, PVR > 3 Wood Units, or  PH-HFpEF with exercise, defined as peak mean PAOP > 17, peak mean PAP > 30, peak PVR > 1.34 Wood Units if age < 50 or peak mean PAOP > 19, peak mean PAP > 33, and PVR < 2.1 Wood Units if age >= 50  The subject also must meet criteria for metabolic syndrome, defined as: Abdominal obesity (BMI > 30 kg/m2 or abdominal obesity, waist circumference > 102 cm men, > 88 cm women) AND 2 of the following;  a. Currently being treated for systemic hypertension or blood pressure (BP) >= 135/85 b. Glucose intolerance with diagnosis of type 2 diabetes, or fasting blood glucose 110-125 mg/dL or hemoglobin A1c > 6% c. Triglycerides >= 150, or on treatment for high triglycerides d. HDL < 40 men, < 50 women, or on treatment for high triglycerides  If the subject is on pulmonary hypertension specific vasodilators, they must be on stable medical therapy without changes to pulmonary vasodilator medication within 3 months prior to screening visit. The subject must have also had a cardiopulmonary exercise test within 6 months of screening visit. The subject must have also had an echocardiogram within 6 months of screening visit. The subject must have demonstrated stable weight (less that 5% weight loss) 3 months prior to screening visit. (They cannot already be losing weight). The subject owns and uses a smartphone or tablet. Must speak English  Exclusion Criteria:  The subject is already on a significant weight loss trajectory prior to study entry. The subject cannot be on an alternative diet plan or strategy (e.g., Weight Watchers, Nutrisystem, Ornish). Left ventricular ejection fraction < 50%. Severe valvular disease by echocardiogram or dysfunctional prosthetic valve. Active pericardial disease (moderate or large pericardial effusion or constrictive pericarditis). Active coronary ischemia defined by abnormal stress test, angiogram, or coronary CT angiography per investigator. Prolonged corrected QT interval (QTc) > 450 ms  Significant lung disease on pulmonary function tests (PFT's) within the 6 months of screening visit, (Both post-bronchodilator values and pre-bronchodilator values must meet exclusion criteria. If either post- or pre-bronchodilator values do not, the subject may be included) defined as either:  Irreversible obstructive airways disease (post-bronchodilator forced expiratory volume/forced vital capacity (FEV1/FVC) < 70% predicted) or Restrictive lung disease (FVC < 70% predicted. If total lung capacity (TLC) is >= 70%, it is acceptable to have an FVC of < 70%) or More than mild radiographic pulmonary disease as determine don CT scan within the past 2 years per investigator. History of non-adherence to diuretics within 3 months of screening visit. History or recurrent severe hypokalemia, potassium < 3.0 mg/dL. History of kidney stones, gout, or gallbladder disease unless in the opinion of the investigator it will not impact the safety of the patient C-peptide < 0.5 ng/mL (increased risk of diabetic ketoacidosis (DKA)) Uncorrected anemia (hemoglobin < 10 g/dL). Unable to participate in the comprehensive ketogenic diet program, including biometric data acquisition and data entry (glucometer self-stick and smartphone use). Unable or unwilling to prepare meals for self. Unable to perform quantitative cardia testing regimen (cardiopulmonary exercise testing, 6-minute walk). Subject is pregnant or planning to become pregnant in the next 14 months.